BEGIN:VCALENDAR VERSION:2.0 PRODID:-//CERN//INDICO//EN BEGIN:VEVENT SUMMARY:A sharp BMO-BLO bound for the martingale maximal function DTSTART;VALUE=DATE-TIME:20210702T133000Z DTEND;VALUE=DATE-TIME:20210702T140000Z DTSTAMP;VALUE=DATE-TIME:20260414T002242Z UID:indico-contribution-321-232@indico.eimi.ru DESCRIPTION:Speakers: Leonid Slavin (University of Cincinnati)\nWe constru ct the exact Bellman function for the BMO-BLO action of the natural martin gale maximal function for continuous-time martingales. (BLO stands for "bo unded lower oscillation"\; the natural maximal function is the one without the absolute value in the average). As consequences\, we show that the BM O-BLO norm of the operator is 1 and also obtain a sharp weak-type inequali ty\, which can be integrated to produce a broad range of sharp phi-estimat es.\n\nIn an earlier work we found the corresponding Bellman function for alpha-regular discrete-time martingales\, including the dyadic martingale. I will discuss the essential differences between the two cases. This is j oint work with Adam Osekowski and Vasily Vasyunin.\n\nhttps://indico.eimi. ru/event/321/contributions/232/ LOCATION: URL:https://indico.eimi.ru/event/321/contributions/232/ END:VEVENT BEGIN:VEVENT SUMMARY:Introductory word DTSTART;VALUE=DATE-TIME:20210705T073000Z DTEND;VALUE=DATE-TIME:20210705T075000Z DTSTAMP;VALUE=DATE-TIME:20260414T002242Z UID:indico-contribution-321-231@indico.eimi.ru DESCRIPTION:Speakers: Sergei Kislyakov (St.Petersburg Department of Steklo v Institute)\nhttps://indico.eimi.ru/event/321/contributions/231/ LOCATION: URL:https://indico.eimi.ru/event/321/contributions/231/ END:VEVENT BEGIN:VEVENT SUMMARY:Pointwise convergence of scattering data DTSTART;VALUE=DATE-TIME:20210705T125500Z DTEND;VALUE=DATE-TIME:20210705T134000Z DTSTAMP;VALUE=DATE-TIME:20260414T002242Z UID:indico-contribution-321-230@indico.eimi.ru DESCRIPTION:Speakers: Alexei Poltoratski (University of Wisconsin-Madison) \nThe scattering transform\, appearing in the study of differential operat ors\, can be viewed as an analog of the Fourier transform in non-linear se ttings. This connection brings up numerous questions on finding non-linear analogs of classical results of Fourier analysis. One of the fundamental results of linear analysis is a theorem by L. Carleson on pointwise conver gence of the Fourier series. In this talk I will discuss convergence for t he scattering data of a real Dirac system on the half-line and present an analog of Carleson's theorem for the non-linear Fourier transform.\n\nhttp s://indico.eimi.ru/event/321/contributions/230/ LOCATION: URL:https://indico.eimi.ru/event/321/contributions/230/ END:VEVENT BEGIN:VEVENT SUMMARY:Orthogonality in Banach spaces DTSTART;VALUE=DATE-TIME:20210705T141500Z DTEND;VALUE=DATE-TIME:20210705T150000Z DTSTAMP;VALUE=DATE-TIME:20260414T002242Z UID:indico-contribution-321-229@indico.eimi.ru DESCRIPTION:Speakers: Alexander Volberg (Michigan State University)\nAll s paces below are not Hilbert spaces. Given two finite dimensional subspaces $L\, K$ of a normed space $X$ we call $K$ orthogonal to $L$ if for every unit vector in $K$ the distance of this vector to $L$ is $1$.\n\nThis usu ally does not mean that $L$ is orthogonal to $K$.\n\nWe consider the follo wing questions: 1) Let $E\, F$ are two finite dimensional subspaces of a n ormed space $X$ and let $dim F= dim E+m$. Can we always find a subspace $ K$ in $F$ such that $E$ is orthogonal to $K$? 2) Can we always find a subs pace $K$ in $F$ such that $K$ is orthogonal to $E$? 3) Can we always choos e $K$ of dimension $m$? 4) If not\, what is the maximal possible dimension ? \n\nThese questions seem to be considered 60-80 years ago\, and in fact\ , some of them were answered (by Krein--Krasnoselski--Milman). But it look s like that some of these questions were overlooked...\n\nhttps://indico.e imi.ru/event/321/contributions/229/ LOCATION: URL:https://indico.eimi.ru/event/321/contributions/229/ END:VEVENT BEGIN:VEVENT SUMMARY:Landis’ conjecture on the decay of solutions to Schrödinger equ ations on the plane DTSTART;VALUE=DATE-TIME:20210705T151000Z DTEND;VALUE=DATE-TIME:20210705T155500Z DTSTAMP;VALUE=DATE-TIME:20260414T002242Z UID:indico-contribution-321-228@indico.eimi.ru DESCRIPTION:Speakers: Eugenia Malinnikova (Stanford University)\nWe consid er a real-valued function on the plane for which the absolute value of the Laplacian is bounded by the absolute value of the function at each point. In other words\, we look at solutions of the stationary Schrödinger equa tion with a bounded potential. The question discussed in the talk is how f ast such function may decay at infinity. We give the answer in dimension t wo\, in higher dimensions the corresponding problem is open.\n\n The talk is based on the joint work with A. Logunov\, N. Nadirashvili\, and F. Naza rov.\n\nhttps://indico.eimi.ru/event/321/contributions/228/ LOCATION: URL:https://indico.eimi.ru/event/321/contributions/228/ END:VEVENT BEGIN:VEVENT SUMMARY:Completely bounded Schur multipliers of Schatten-von Neumann class $S_p\, 0 < p < 1$. DTSTART;VALUE=DATE-TIME:20210705T120000Z DTEND;VALUE=DATE-TIME:20210705T124500Z DTSTAMP;VALUE=DATE-TIME:20260414T002242Z UID:indico-contribution-321-227@indico.eimi.ru DESCRIPTION:Speakers: Vladimir Peller (Michigan State University)\nI am go ing to speak about my joint results with A.B. Aleksandrov. Gilles Pisier p osed the problem of whether a matrix Schur multiplier of the Schatten—vo n Neumann class $S_p$ for $1 < p < \\infty$\, $p\\neq 2$\, has to be compl etely bounded. We have proved that this is true in the case $0< p < 1$. We also consider various sufficient conditions for an infinite matrix to be a Schur multiplier of $S_p$. In particular\, we introduce a $p$-analog of the Haagerup tensor product of $\\ell^\\infty$ spaces.\n\nhttps://indico.e imi.ru/event/321/contributions/227/ LOCATION: URL:https://indico.eimi.ru/event/321/contributions/227/ END:VEVENT BEGIN:VEVENT SUMMARY:Contractive inequalities for Hardy spaces DTSTART;VALUE=DATE-TIME:20210705T092000Z DTEND;VALUE=DATE-TIME:20210705T100500Z DTSTAMP;VALUE=DATE-TIME:20260414T002242Z UID:indico-contribution-321-226@indico.eimi.ru DESCRIPTION:Speakers: Kristian Seip ()\nIt has been recognized by many aut hors that contractive inequalities involving norms of $H^p$ spaces can be particularly useful when the objects in question (like the norms and/or an underlying operator) lift in a multiplicative way from one (or few) to se veral (or infinitely many) variables. This has been my main motivation for looking more systematically at various contractive inequalities in the co ntext of Hardy spaces on the $d$-dimensional torus. I will discuss results from recent studies of Hardy--Littlewood inequalities\, Riesz projections \, idempotent Fourier multipliers\, and Hilbert points (which in one varia ble is another word for inner functions). We will see interesting phenomen a occurring both in the transition from low to high dimension and from low to infinite dimension. The talk builds on joint work with Sergei Konyagin \, Herve Queffelec\, and Eero Saksman and with Ole Fredrik Brevig and Joaq uim Ortega-Cerda.\n\nhttps://indico.eimi.ru/event/321/contributions/226/ LOCATION: URL:https://indico.eimi.ru/event/321/contributions/226/ END:VEVENT BEGIN:VEVENT SUMMARY:Inequalities involving Hardy spaces of Musielak type DTSTART;VALUE=DATE-TIME:20210705T080000Z DTEND;VALUE=DATE-TIME:20210705T084500Z DTSTAMP;VALUE=DATE-TIME:20260414T002242Z UID:indico-contribution-321-225@indico.eimi.ru DESCRIPTION:Speakers: Aline Bonami (Orleans University)\nThe space $H^{\\l og}$ has been introduced in relation with the product of functions $f\\tim es g$ (in the distributional sense) such that $f$ belongs to $H^1(\\mathbb R^d)$ and $g$ belongs to $BMO(\\mathbb R^d).$ Since then\, Hardy spaces o f Musielak type have been the object of many studies\, as well as generali zations of inequalities involving products. I will discuss some of them an d characterize non-negative $L^1$ functions that belong to $H^{\\log}(\\ma thbb R^d)$ and other Hardy spaces of Musielak type.\n\nPart of this is wor k in progress with S. Grellier and B. Sehba.\n\nhttps://indico.eimi.ru/eve nt/321/contributions/225/ LOCATION: URL:https://indico.eimi.ru/event/321/contributions/225/ END:VEVENT BEGIN:VEVENT SUMMARY:The Dirichlet space on the bi-disc DTSTART;VALUE=DATE-TIME:20210703T113000Z DTEND;VALUE=DATE-TIME:20210703T121000Z DTSTAMP;VALUE=DATE-TIME:20260414T002242Z UID:indico-contribution-321-224@indico.eimi.ru DESCRIPTION:Speakers: Nikola Arcozzi (University of Bologna)\nThe Dirichle t space on the bidisc can be informally defined as the tensor product $\\m athcal{D} (\\mathbb{D}^2) =\\mathcal{D} (\\mathbb{D}) \\otimes \\mathcal{D } (\\mathbb{D})$ of two copies of the classical holomorphic Dirichlet spac e. Multipliers and Carleson measures for the space were recently character ized\, and the results have been extended to the three-disc\, but not to h igher powers. Underlying all this there is a new multi-parameter potential theory which is still in its infancy\, and many basic problems await an a nswer. The talk reports on work by several authors: Pavel Mozolyako\, Karl -Mikael Perfekt\, Giulia Sarfatti\, Irina Holmes\, Alexander Volberg\, Geo rgios Psaromiligkos\, Pavel Zorin-Kranich\, and the speaker.\n\nhttps://in dico.eimi.ru/event/321/contributions/224/ LOCATION: URL:https://indico.eimi.ru/event/321/contributions/224/ END:VEVENT BEGIN:VEVENT SUMMARY:On perturbations of semigroups based upon operator-valued measures DTSTART;VALUE=DATE-TIME:20210703T143500Z DTEND;VALUE=DATE-TIME:20210703T150500Z DTSTAMP;VALUE=DATE-TIME:20260414T002242Z UID:indico-contribution-321-222@indico.eimi.ru DESCRIPTION:Speakers: Grigorii Amosov (Steklov Mathematical Institute of R AS)\nSuppose that $S_t:\\ X\\to X\,\\ t\\ge 0\,$ is a $C_0$-semigroup on t he Banach space $X$. Consider the covariant operator-valued measure $\\mat hcal M$ on the half-axis ${\\mathbb R}_+$ taking values in operators on $X $ and satisfying the property\n$$\nS_t\\circ {\\mathcal M}(B)={\\mathcal M }(B+t)\,\\ t\\ge 0\,\n$$\nfor all measurable subsets $B \\subset \\mathbb R_+$. \n\nTheorem. Suppose that ${\\mathcal M}$ is semi-absolutely continu ous in the sense\n$$\n\\lim \\limits _{t\\to +0}\\overline {\\mathcal M}([ T\,T+t))=0\,\\ \\forall T\\ge 0\,\n$$ \nwhere\n$$\n\\overline{\\mathcal M} (E) = \\sup\\Bigl\\{\\Bigl\\| \\sum_{i=1}^n {\\mathcal M}(E_i)x_i\\Bigr\\| : x_j\\in X\,\\|x_j\\|\\le 1\, E\\supset E_j\\subset {\\mathbb R}\, E_j\\m box{ are disjoint}\\Bigr\\}\n$$\nfor all measurable $E\\subset {\\mathbb R }_+$. Then\, the solution to the integral equation\n$$\n\\breve S_t=S_t+\\ int \\limits _0^t{\\mathcal M}(ds)\\circ \\breve S_{t-s}\n$$\nproduce the $C_0$-semigroup $\\breve S=\\{\\breve S_t\,\\ t\\ge 0\\}$. The generator o f $\\breve S$ acts as\n$$\nx\\to \\lim\\limits _{t\\to +0}\\frac {S_t-I+{\ \mathcal M}([0\,t))}{t}x\n$$\nwith the domain consisting of exactly those $x$ for which the strong limit exists.\n\nMeaningful examples of covariant measures can be obtained from the orbits of unitary groups in infinite-di mensional space [1].\n\nThis work was funded by Russian Federation represe nted by the Ministry of Science\nand Higher Education of the Russian Feder ation (Grant No. 075-15-2020-788) and\nperformed at the Steklov Mathematic al Institute of the Russian Academy of Sciences.\n\nJoint work with E.L. B aitenov. \n\n[1] G. G. Amosov\, A. S. Mokeev\, A. N. Pechen\, Noncommutati ve graphs based on finite-infinite system couplings: Quantum error correct ion for a qubit coupled to a coherent field\, Phys. Rev. A\, 103:4 (2021)\ , 042407\, 17 pp.\n\nhttps://indico.eimi.ru/event/321/contributions/222/ LOCATION: URL:https://indico.eimi.ru/event/321/contributions/222/ END:VEVENT BEGIN:VEVENT SUMMARY:Boundedness of Bergman projections on homogeneous Siegel domains DTSTART;VALUE=DATE-TIME:20210703T131000Z DTEND;VALUE=DATE-TIME:20210703T135000Z DTSTAMP;VALUE=DATE-TIME:20260414T002242Z UID:indico-contribution-321-221@indico.eimi.ru DESCRIPTION:Speakers: Marco Peloso (Università degli Studi di Milano)\nIn this talk I will discuss the problem of boundedness of the Bergman projec tion on Bergman spaces on homogeneous Siegel domains of Type II. It was sh own that in the case of tube domains over symmetric cone\, that is\, symme tric Siegel domains of Type I\, the Bergman projection $P$ may be bounde d even if the operator $P_+$\, having as integral kernel the modulus of th e Bergman kernel\, is unbounded. I will describe what is known in this ca se and then discuss the case of homogeneous Siegel domains of Type II. I w ill discuss equivalent conditions\, such as characterization of boundary v alues\, duality\, Hardy-type inequalities. This is a report on joint work with M. Calzi.\n\nhttps://indico.eimi.ru/event/321/contributions/221/ LOCATION: URL:https://indico.eimi.ru/event/321/contributions/221/ END:VEVENT BEGIN:VEVENT SUMMARY:The quadric models in CR geometry DTSTART;VALUE=DATE-TIME:20210706T091500Z DTEND;VALUE=DATE-TIME:20210706T094500Z DTSTAMP;VALUE=DATE-TIME:20260414T002242Z UID:indico-contribution-321-220@indico.eimi.ru DESCRIPTION:Speakers: Valerii Beloshapka (Lomonosov Moscow State Universit y)\nDuring last 30 years it was supposed that the graded Lie algebra of in finitesimal holomorphic automorphisms of quadric model CR manifold hasn't nontrivial graded components of weight greater than two. Recently it turne d out that it is not true. There exist some enigmatic “special” quadri cs\, whose graded components go further. The author is going to speak abou t his recent advances in the understanding of this phenomenon. \nThe main results was obtained with the help of distributions\, Fourier transform an d the fundamental principle of Ehrenpreis.\n\nhttps://indico.eimi.ru/event /321/contributions/220/ LOCATION: URL:https://indico.eimi.ru/event/321/contributions/220/ END:VEVENT BEGIN:VEVENT SUMMARY:On the Hankel transform of functions from Nikol'skii type classes DTSTART;VALUE=DATE-TIME:20210706T084000Z DTEND;VALUE=DATE-TIME:20210706T091000Z DTSTAMP;VALUE=DATE-TIME:20260414T002242Z UID:indico-contribution-321-219@indico.eimi.ru DESCRIPTION:Speakers: Sergey Platonov (Petrozavovsk State University)\nLet a function $f$ belongs to the Lebesgue class $L_p({\\mathbb R})$\, $1\\le p\\le 2$\, and let $\\widehat{f}$ be the Fourier transform of $f$. The cl assical theorem of E.Titchmarsh states that if the function $f$ belongs to the Lipschitz class $Lip(r\,p\; {\\mathbb R})$\, $0 < r\\le 1$\, then $\\ hat f$ belongs to the Lebesgue classes $L_q({\\mathbb R})$ for $\\frac{p}{ r p+p-1}< q\\le \\frac{p}{p-1}$. Using the methods of Fourier-Bessel harmo nic analysis we prove an analogue of this result for the the Hankel transf orm of functions from Nikol'skii type function classes on the half-line $[ 0\,+\\infty)$.\n\nhttps://indico.eimi.ru/event/321/contributions/219/ LOCATION: URL:https://indico.eimi.ru/event/321/contributions/219/ END:VEVENT BEGIN:VEVENT SUMMARY:Gabor analysis for rational functions DTSTART;VALUE=DATE-TIME:20210704T084000Z DTEND;VALUE=DATE-TIME:20210704T092000Z DTSTAMP;VALUE=DATE-TIME:20260414T002242Z UID:indico-contribution-321-218@indico.eimi.ru DESCRIPTION:Speakers: Yurii Belov (Saint-Petersburg State University)\nLet $g$ be a function in $L^2(\\mathbb{R})$. By $G_\\Lambda$\, $\\Lambda\\sub set R^2$\, we denote the system of time-frequency shifts of $g$\, $G_\\La mbda=\\{e^{2\\pi i \\omega x}g(x-t)\\}_{(t\,\\omega)\\in\\Lambda}$. A typi cal model set $\\Lambda$ is the rectangular lattice $\\Lambda_{\\alpha\, \\beta}:= \\alpha\\mathbb{Z}\\times\\beta\\mathbb{Z}$ and one of the basi c problems of the Gabor analysis is the description of the frame set of $ g$ i.e.\, all pairs $\\alpha\, \\beta$ such that $G_{\\Lambda_{\\alpha\,\ \beta}}$ is a frame in $L^2(\\mathbb{R})$. It follows from the general the ory that $\\alpha\\beta \\leq 1$ is a necessary condition (we assume $\\al pha\, \\beta > 0$\, of course). Do all such $\\alpha\, \\beta $ belong to the frame set of $g$?\n \nUp to 2011 only few such functions $g$ (up to t ranslation\, modulation\, dilation and Fourier transform) were known. In 2 011 K. Grochenig and J. Stockler extended this class by including the tot ally positive functions of finite type (uncountable family yet depending o n finite number of parameters) and later added the Gaussian finite type to tally positive functions. We suggest another approach to the problem and p rove that all Herglotz rational functions with imaginary poles also belo ng to this class. This approach also gives new results for general ratio nal functions. In particular\, we are able to confirm Daubechies conjectur e for rational functions and irrational densities.\n\nJoint work with Yu. Lyubarskii and A. Kulikov\n\nhttps://indico.eimi.ru/event/321/contribution s/218/ LOCATION: URL:https://indico.eimi.ru/event/321/contributions/218/ END:VEVENT BEGIN:VEVENT SUMMARY:On the Fourier-Laplace transform of functionals on a space of ult radifferentiable functions on a convex compact DTSTART;VALUE=DATE-TIME:20210704T092500Z DTEND;VALUE=DATE-TIME:20210704T095500Z DTSTAMP;VALUE=DATE-TIME:20260414T002242Z UID:indico-contribution-321-217@indico.eimi.ru DESCRIPTION:Speakers: Il'dar Musin (Institute of Mathematics with Computer Centre of Ufa Scientific Centre of RAS)\nClasses of ultradifferentiable f unctions are classically defined by imposing growth conditions on the deri vatives of the functions. Following this approach we consider a Fr\\'echet -Schwartz space of infinitely differentiable functions on a closure of a b ounded convex domain of multidimensional real space with uniform bounds on their partial derivatives. The main aim is to obtain Paley-Wiener-Schwart z type theorem connecting properties of linear continuous functionals on t his space with the behaviour of their Fourier-Laplace transforms. Very sim ilar problems were considered by M. Neymark\, B.A. Taylor\, M. Langenbruch \, A.V. Abanin. Also some applications of this theorem to PDE and their sy stems will be given.\n\nhttps://indico.eimi.ru/event/321/contributions/217 / LOCATION: URL:https://indico.eimi.ru/event/321/contributions/217/ END:VEVENT BEGIN:VEVENT SUMMARY:Composition of analytic paraproducts DTSTART;VALUE=DATE-TIME:20210701T084500Z DTEND;VALUE=DATE-TIME:20210701T092500Z DTSTAMP;VALUE=DATE-TIME:20260414T002242Z UID:indico-contribution-321-216@indico.eimi.ru DESCRIPTION:Speakers: Alexandru Aleman (University of Lund)\nFor a fixed analytic function $g$ in the unit disc\, we consider the analytic parapro ducts induced by $g$\, which are defined by $T_gf(z)= \\int_0^z f(\\zeta)g '(\\zeta)\\\,d\\zeta$\, $S_gf(z)= \\int_0^z f'(\\zeta)g(\\zeta)\\\,d\\zeta $\, together with the multiplication operator $M_gf(z)= f(z)g(z)$. The bou ndedness of these operators on various spaces of analytic functions on the unit disc is well understood. The original motivation for this work is to understand the boundedness of compositions (products) of two of these ope rators\, for example $T_g^2\, \\\,T_gS_g\,\\\, M_gT_g$\, etc. The talk i ntends to present a general approach which yields a characterization of t he boundedness of a large class of operators contained in the algebra generated by these analytic paraproducts acting on the classical weighte d Bergman and Hardy spaces in terms of the symbol $g$. In some cases it tu rns out that this property is not affected by cancellation\, while in oth ers it requires stronger and more subtle restrictions on the oscillation o f the symbol $g$ than the case of a single paraproduct. This is a report about joint work with C. Cascante\, J. F\\`abrega\, D. Pascua and J.A. Pel \\'aez\n\nhttps://indico.eimi.ru/event/321/contributions/216/ LOCATION: URL:https://indico.eimi.ru/event/321/contributions/216/ END:VEVENT BEGIN:VEVENT SUMMARY:Polynomial approximation in a convex domain in $\\mathbb{C}^n$ whi ch is exponentially decreasing inside the domain DTSTART;VALUE=DATE-TIME:20210701T144000Z DTEND;VALUE=DATE-TIME:20210701T150000Z DTSTAMP;VALUE=DATE-TIME:20260414T002242Z UID:indico-contribution-321-215@indico.eimi.ru DESCRIPTION:Speakers: Nikolai Shirokov (St.-Petersburg State University an d National Research University High School of Economics in SPb)\nLet $\\Om ega\\subset \\mathbb{C}^n$\, $n\\ge 2$\, be a bounded convex domain with t he $C^2$-smooth boundary. We suppose that $\\Omega$ satisfies some propert ies. The strictly convex in the analytical sense domains satisfy those pro perties. It is proved that for any function $f$ holomorphic is $\\Omega$ a nd smooth in $\\bar{\\Omega}$ there exist polynomials $P_N$\, $\\deg P_N\\ leq N$ such that $\\bigl|f(z)-P_N(z)\\bigr|$ has the polynomial decay for $z\\in \\partial\\Omega$ and the exponential decay when $z$ lies strictly inside $\\Omega$.\n\nhttps://indico.eimi.ru/event/321/contributions/215/ LOCATION: URL:https://indico.eimi.ru/event/321/contributions/215/ END:VEVENT BEGIN:VEVENT SUMMARY:Riesz bases of normalized reproducing kernels in radial Hilbert sp aces of entire functions DTSTART;VALUE=DATE-TIME:20210702T092500Z DTEND;VALUE=DATE-TIME:20210702T095500Z DTSTAMP;VALUE=DATE-TIME:20260414T002242Z UID:indico-contribution-321-214@indico.eimi.ru DESCRIPTION:Speakers: Rinad Yulmukhametov (Institute of Mathematics with C omputing Centre - Subdivision of the Ufa Federal Research Centre of Russia n Academy of Science)\nWe consider a reproducing kernel radial Hilbert spa ce of entire functions and prove necessary and sufficient conditions for t he existence of unconditional bases of reproducing kernels in terms of nor ms of monomials. The results obtained are applied to weighted Fock spaces. \n\nhttps://indico.eimi.ru/event/321/contributions/214/ LOCATION: URL:https://indico.eimi.ru/event/321/contributions/214/ END:VEVENT BEGIN:VEVENT SUMMARY:Functions with small and large spectra as (non)extreme points in s ubspaces of $H^\\infty$ DTSTART;VALUE=DATE-TIME:20210701T075000Z DTEND;VALUE=DATE-TIME:20210701T082000Z DTSTAMP;VALUE=DATE-TIME:20260414T002242Z UID:indico-contribution-321-213@indico.eimi.ru DESCRIPTION:Speakers: Konstantin Dyakonov (ICREA and Universitat de Barcel ona)\nLet $\\Lambda$ be a subset of $\\mathbb Z_+:=\\{0\,1\,2\,\\dots\\}$\ , and let $H^\\infty(\\Lambda)$ denote the space of bounded analytic funct ions $f$ on the disk whose coefficients $\\hat f(k)$ vanish for $k\\notin\ \Lambda$. Assuming that either $\\Lambda$ or $\\mathbb Z_+\\setminus\\Lamb da$ is finite\, we determine the extreme points of the unit ball in $H^\\i nfty(\\Lambda)$.\n\nhttps://indico.eimi.ru/event/321/contributions/213/ LOCATION: URL:https://indico.eimi.ru/event/321/contributions/213/ END:VEVENT BEGIN:VEVENT SUMMARY:Calderon-Zygmund operators on RBMO DTSTART;VALUE=DATE-TIME:20210704T120000Z DTEND;VALUE=DATE-TIME:20210704T122000Z DTSTAMP;VALUE=DATE-TIME:20260414T002242Z UID:indico-contribution-321-212@indico.eimi.ru DESCRIPTION:Speakers: Evgueni Doubtsov (St. Petersburg Department of V.A. Steklov Mathematical Institute)\nLet $\\mu$ be an $n$-dimensional finite p ositive measure on $\\mathbb{R}^m$. We obtain a $T1$ condition sufficient for the boundedness of Calderon-Zygmund operators on $\\textrm{RBMO}(\\mu) $\, the regular BMO space of Tolsa. (Joint work with Andrei V. Vasin.)\n\n https://indico.eimi.ru/event/321/contributions/212/ LOCATION: URL:https://indico.eimi.ru/event/321/contributions/212/ END:VEVENT BEGIN:VEVENT SUMMARY:An order over the set of analytic functions of two variables DTSTART;VALUE=DATE-TIME:20210704T142000Z DTEND;VALUE=DATE-TIME:20210704T144000Z DTSTAMP;VALUE=DATE-TIME:20260414T002242Z UID:indico-contribution-321-211@indico.eimi.ru DESCRIPTION:Speakers: Maria Stepanova (Lomonosov Moscow State University)\ nIn the context of the theory of analytical complexity we can introduce a natural relation «to be not simpler» over the set of germs of analytic functions. The question arises: is that relation an order relation (thre e axioms)? It turns out that the axiom of antisymmetry does not hold. We w ill give an example. Thus\, this relation is only a preorder and turns in to an order only after factorization.\n\nhttps://indico.eimi.ru/event/321/ contributions/211/ LOCATION: URL:https://indico.eimi.ru/event/321/contributions/211/ END:VEVENT BEGIN:VEVENT SUMMARY:On linear extremal problems in the classes of nonvanishing bound ed analytic functions. DTSTART;VALUE=DATE-TIME:20210701T123500Z DTEND;VALUE=DATE-TIME:20210701T130500Z DTSTAMP;VALUE=DATE-TIME:20260414T002242Z UID:indico-contribution-321-210@indico.eimi.ru DESCRIPTION:Speakers: Ilgiz Kayumov (Kazan (Volga Region) Federal Universi ty)\nI will talk about linear extremal problems in the classes of nonvani shing bounded analytic functions defined in the unit disk centered at the origin. It turns out extremal values in the class of nonvanishing bounded analytic functions can be estimated with the sharp constant $2/e$ from bel ow via extremal values in the whole class of bounded analytic functions.\ n\nhttps://indico.eimi.ru/event/321/contributions/210/ LOCATION: URL:https://indico.eimi.ru/event/321/contributions/210/ END:VEVENT BEGIN:VEVENT SUMMARY:Dirichlet problem for second order elliptic PDE\, and one related approximation problem DTSTART;VALUE=DATE-TIME:20210702T070000Z DTEND;VALUE=DATE-TIME:20210702T074000Z DTSTAMP;VALUE=DATE-TIME:20260414T002242Z UID:indico-contribution-321-208@indico.eimi.ru DESCRIPTION:Speakers: Konstantin Fedorovskiy (Lomonosov Moscow State Unive rsity)\nFirst we plan to discuss the Dirichlet problem for second order ho mogeneous elliptic equations with constant complex coefficients in domains in the complex plane. We will present and discuss the following result: e very Jordan domain in $\\mathbb C$ with $C^{1\,\\alpha}$-smooth boundary\, $\\alpha\\in(0\,1)$\, is not regular with respect to the Dirichlet proble m for any not strongly elliptic equation of the specified type. Next we wi ll touch the problem on uniform approximation of functions on compact sets in the complex plane by polynomial solutions of such equations. We presen t some recent results and open questions concerning this problem and its l inks with the Dirichlet problems under consideration. \n\n*The talk is bas ed on a joint work with A. Bagapsh and M. Mazalov*\n\nhttps://indico.eimi. ru/event/321/contributions/208/ LOCATION: URL:https://indico.eimi.ru/event/321/contributions/208/ END:VEVENT BEGIN:VEVENT SUMMARY:Two-sided estimates for band lengths of Laplacians on periodic gra phs DTSTART;VALUE=DATE-TIME:20210701T120000Z DTEND;VALUE=DATE-TIME:20210701T123000Z DTSTAMP;VALUE=DATE-TIME:20260414T002242Z UID:indico-contribution-321-207@indico.eimi.ru DESCRIPTION:Speakers: Evgeny Korotyaev (St Petersburg University\, Higher school of economics)\nWe consider Laplacians on periodic discrete graphs. Their spectrum consists of a finite number of bands. We obtain two-sided e stimates for the total length of the spectral bands of the Laplacian in t erms of geometric parameters of the graph. Moreover\, we consider Schr\\"o dinger operators with periodic potentials on periodic discrete graphs. We obtain two-sided estimates for the total length of the spectral bands of the operators in terms of geometric parameters of the graph and the potent ial. The proof is based on the Floquet theory and the trace formulas fo r fiber operators. In particular\, we show that these estimates are sharp. It means that these estimates become identities for specific graphs and potentials. Joint work with N.Saburova\n\nhttps://indico.eimi.ru/event/321 /contributions/207/ LOCATION: URL:https://indico.eimi.ru/event/321/contributions/207/ END:VEVENT BEGIN:VEVENT SUMMARY:Interpolation by Jones-Type Series in Spaces of Analytic Functions in the Half-Plane DTSTART;VALUE=DATE-TIME:20210706T070000Z DTEND;VALUE=DATE-TIME:20210706T074000Z DTSTAMP;VALUE=DATE-TIME:20260414T002242Z UID:indico-contribution-321-206@indico.eimi.ru DESCRIPTION:Speakers: Konstantin Malyutin (Kursk State University\, Russia )\nDenote by $\\mathcal{A}_+$ the space of analytic functions in the upper half-plane $\\mathbb{C}_+=\\{z:\\Im z>0\\}$\, where $\\mathcal{A}_+$ is o ne of the spaces: 1) the space functions of finite order $\\rho>1$\, 2) th e space functions of finite order $\\rho>0$ and of normal type\, 3) the sp ace of bounded functions $H^\\infty$.\nLet $D=\\{a_n\,q_n\\}_{n=1}^\\infty \,$ be a divisor (i.e.\, a set of distinct complex numbers $\\{a_n\\}_{n=1 }^\\infty\\subset\\mathbb{C}_+$ with limit points on the real axis\, toget her with their integer multiplicities $\\{q_n\\}_{n=1}^\\infty\\subset\\ma thbb N$). In the space \n $\\mathcal{A}_+$\, the interpolation problem is considered:\n$$\nF^{(k-1)}(a_n)=b_{n\,k}\,\\quad k=1\,2\,\\dots\,q_n\,\\> n\\in\\mathbb N\\\,\\quad F\\in\\mathcal{A}_+.\n$$\nWe find a criterion fo r the interpolation of the divisor $D$ in the spaces $\\mathcal{A}_+$ in t erms of canonical products and in terms of the Nevanlinna measure $\\mu_+( G)=\\sum_{a_n\\in G}q_n\\sin(\\arg a_n)$ defined by the interpolation node s.\nThe solution to the problem is constructed in the form of a Jones-type interpolation series. \nThis method is also used to solve interpolation p roblems in spaces of meromorphic functions in a half-plane with a given gr owth.\n\nhttps://indico.eimi.ru/event/321/contributions/206/ LOCATION: URL:https://indico.eimi.ru/event/321/contributions/206/ END:VEVENT BEGIN:VEVENT SUMMARY:Dominating Sets in Bergman Spaces on Domains in C^n DTSTART;VALUE=DATE-TIME:20210703T151000Z DTEND;VALUE=DATE-TIME:20210703T153000Z DTSTAMP;VALUE=DATE-TIME:20260414T002242Z UID:indico-contribution-321-204@indico.eimi.ru DESCRIPTION:Speakers: Walton Green (Washington University in St. Louis)\nW e obtain local estimates (also called propogation of smallness\, or Remez- type inequalities) for analytic functions in several variables. Using Carl eman estimates\, we obtain a three sphere-type inequality\, where the oute r two spheres can be any sets satisfying a boundary separation property\, and the inner sphere can be any set of positive Lebesgue measure. We apply this local result to characterize the dominating sets for Bergman spaces on strongly pseudo-convex domains and give a sufficient condition on more general domains.\n\nhttps://indico.eimi.ru/event/321/contributions/204/ LOCATION: URL:https://indico.eimi.ru/event/321/contributions/204/ END:VEVENT BEGIN:VEVENT SUMMARY:On singular spectrum of $N$-dimensional perturbations (to the Aron szajn-Donoghue-Kac theory) DTSTART;VALUE=DATE-TIME:20210701T140500Z DTEND;VALUE=DATE-TIME:20210701T143500Z DTSTAMP;VALUE=DATE-TIME:20260414T002242Z UID:indico-contribution-321-203@indico.eimi.ru DESCRIPTION:Speakers: Mark Malamud (Peoples Friendship University of Russi a (RUDN University))\nThe main results of the Aronszajn-Donoghue-Kac theo ry are extended to the case of $n$-dimensional (in the resolvent sense) p erturbations $\\widetilde A$ of an operator $A_0=A^*_0$ defined on a Hilbe rt space $\\frak H$. Applying technique of boundary triplets we describe singular continuous and point spectra of extensions $A_B$ of a simple s ymmetric operator $A$ acting in $\\frak H$ in terms of the Weyl function $ M(\\cdot)$ of the pair $\\{A\,A_0\\}$ and a boundary $n$-dimensional ope rator $B = B^*$. Assuming that the multiplicity of singular spectrum of $A_0$ is maximal it is established that the singular parts $E^s_{A_B}$ and $E^s_{A_0}$ of the spectral measures $E_{A_B}$ and $E_{A_0}$ of the operators $A_B$ and $A_0$\, respectively\, are mutually singular. We also obtain estimates of the multiplicity of point and singular continuous sp ectra of selfadjoint extensions of $A$.\n\nApplying this result to direct sums $A = A^{(1)}\\oplus A^{(2)}$ allow us to generalize and clarify K ac theorem on multiplicity of singular spectrum of Schr\\"odinger operator on the line. Applications to differential operators will be also discusse d. The talk is based on results announced in [1].\n\n[1] Malamud M.M.\, D oklady Math.\, On Singular Spectrum of Finite-Dimensional Perturbations (t oward the Aronszajn–Donoghue–Kac Theory)\, 2019\, Vol. 100\, No. 1\, p. 358–362.\n\nhttps://indico.eimi.ru/event/321/contributions/203/ LOCATION: URL:https://indico.eimi.ru/event/321/contributions/203/ END:VEVENT BEGIN:VEVENT SUMMARY:Asymptotical behavior of the conformal modulus of doubly connected planar domain under unbounded stretching along the abscissa axis DTSTART;VALUE=DATE-TIME:20210701T133000Z DTEND;VALUE=DATE-TIME:20210701T140000Z DTSTAMP;VALUE=DATE-TIME:20260414T002242Z UID:indico-contribution-321-202@indico.eimi.ru DESCRIPTION:Speakers: Semen Nasyrov (Kazan Federal University)\nConformal moduli of doubly connected domains and quadrilaterals play an important ro le in investigation of various problems of the theory of conformal and qua siconformal mappings. One of the simplest quasiconformal mappings is the s tretching along the abscissa axis. In 2005 Prof. Vourinen suggested the pr oblem of finding the asymptotics of the conformal modulus of a doubly conn ected planar domain under stretching it along the abscissa axis\, as the c oefficient of stretching tends to infinity. We discuss the problem in the cases of bounded and unbounded domains and\, for some types of domains\, f ind the main term of the asymptotics. Our study is based on the methods of geometric functions of a complex variable\, in particular\, on some resul ts by Ahlfors and Warshavskii.\n\nhttps://indico.eimi.ru/event/321/contrib utions/202/ LOCATION: URL:https://indico.eimi.ru/event/321/contributions/202/ END:VEVENT BEGIN:VEVENT SUMMARY:Inverse resonance problem for Dirac operators on the half-line DTSTART;VALUE=DATE-TIME:20210704T135500Z DTEND;VALUE=DATE-TIME:20210704T141500Z DTSTAMP;VALUE=DATE-TIME:20260414T002242Z UID:indico-contribution-321-201@indico.eimi.ru DESCRIPTION:Speakers: Dmitrii Mokeev (Higher School of Economics)\nWe cons ider massless Dirac operators on the half-line with compactly supported po tentials. We solve the inverse problems in terms of Jost function and scat tering matrix (including characterization). We study resonances as zeros o f Jost function and prove that they uniquely determine a potential of the Dirac operator. We also estimate the forbidden domain for resonances and d etermine asymptotics of resonance counting function. At last we show how t hese results are applied to canonical systems. The talk is based on joint work with Evgeny Korotyaev.\n\nhttps://indico.eimi.ru/event/321/contributi ons/201/ LOCATION: URL:https://indico.eimi.ru/event/321/contributions/201/ END:VEVENT BEGIN:VEVENT SUMMARY:Equiangular Tight Frames as Dictionaries in Sparse Representations DTSTART;VALUE=DATE-TIME:20210702T123500Z DTEND;VALUE=DATE-TIME:20210702T130500Z DTSTAMP;VALUE=DATE-TIME:20260414T002242Z UID:indico-contribution-321-199@indico.eimi.ru DESCRIPTION:Speakers: Sergei Novikov (Samara National Research University) \nLet $\\mathbf{\\Phi}$ be $d\\times n$-matrix with real or complex number s\, and the columns of $\\mathbf{\\Phi}$ are $\\ell_2$-normalized.\n Consi der a linear under-determined set of equations\n $$\n \\mathbf{\\Phi}\\mat hbf{\\alpha}=\\mathbf{x}.\n $$\n We shall refer hereafter to $\\mathbf{x}$ as a signal to be processed\, and $\\mathbf{\\alpha}$ will stand for its {\\it representation}. The matrix $\\mathbf{\\Phi}$ will be referred to as the {\\it dictionary}\, and its columns $\\left\\{\\mathbf{\\varphi}_i\\r ight\\}_{i=1}^n$ will be called {\\it atoms}.\n\nEquiangular tight frames have the important advantage over other dictionaries. In particular\, it' s possible to calculate the spark for such dictionaries.\n\nhttps://indico .eimi.ru/event/321/contributions/199/ LOCATION: URL:https://indico.eimi.ru/event/321/contributions/199/ END:VEVENT BEGIN:VEVENT SUMMARY:On measurable operators affiliated to semifinite von Neumann algeb ras DTSTART;VALUE=DATE-TIME:20210702T120000Z DTEND;VALUE=DATE-TIME:20210702T123000Z DTSTAMP;VALUE=DATE-TIME:20260414T002242Z UID:indico-contribution-321-198@indico.eimi.ru DESCRIPTION:Speakers: Airat Bikchentaev (Kazan Federal University)\nLet $ \\mathcal{M}$ be a von Neumann algebra of operators on a Hilbert space ${ \\mathcal H}$ and $\\tau$ be a faithful normal semifinite trace on ${\\mat hcal M}$. Let $t_{\\tau}$ be the measure topology on the $\\ast$-algebra $S({\\mathcal M}\, \\tau )$ of all $\\tau$-measurable operators. We defi ne three $t_{\\tau}$-closed classes ${\\mathcal P}_1$\, ${\\mathcal P}_2$ and ${\\mathcal P}_3$ of $S({\\mathcal M}\, \\tau )$ with ${\\mathcal P} _1\\cup {\\mathcal P}_3 \\subset {\\mathcal P}_2$ and investigate their pr operties.\n\nIf an operator $T\\in S({\\mathcal M}\, \\tau ) $ is $p$-hy ponormal for $0 < p \\le 1$\, then $T$ lies in ${\\mathcal P}_1$\; if an o perator $T$ lies in ${\\mathcal P}_k$\, then $UTU^*$ belongs to ${\\mathca l P}_k$ for all isometries $U$ from ${\\mathcal M}$ and $k=1\,2\, 3$\; if an operator $T$ from ${\\mathcal P}_1$ admits the bounded inverse $T^{-1 }$ then $T^{-1}$ lies in ${\\mathcal P}_1$. If a bounded operator $T$ lies in $\\mathcal{P}_1\\cup {\\mathcal P}_3$ then $T$ is normaloid. If a n $T\\in S({\\mathcal M}\, \\tau ) $ is hyponormal and $T^n $ is $\\ta u$-compact operator for some natural number $n$ then $T$ is both normal a nd $\\tau$-compact. If an operator $T$ lies in $\\mathcal{P}_1$ then $T ^2$ belongs to $\\mathcal{P}_1$. If $\\mathcal{M}=\\mathcal{B}(\\mathcal{H })$ and $\\tau={\\mathrm tr}$ is the canonical trace\, then the class $ \ \mathcal{P}_1 $ (resp.\, $ \\mathcal{P}_3 $) coincides with the set of al l paranormal (resp.\, $\\ast$-paranormal) operators on $\\mathcal{H}$. Le t $A\, B \\in S({\\mathcal M}\, \\tau )$ and $A$ be $p$-hyponormal with $0 < p \\le 1$. If $AB$ is $\\tau$-compact then $A^*B$ is $\\tau$-compact [1 ]. We also investigate some properties of the Kalton--Sukochev uniform ma jorization in $S({\\mathcal M}\, \\tau )$ [2].\n\nThe work performed under the development program of Volga Region Mathematical Center\n(agreement n o. 075-02-2021-1393).\n\nREFERENCES\n\n1. Bikchentaev A. Paranormal measur able operators affiliated with a semifinite von Neumann algebra. II.\nPosi tivity 24 (2020)\, no. 5\, 1487--1501.\n\n2. Bikchentaev A.\, Sukochev F. Inequalities for the block projection operators. J.\nFunct. Anal. 280 (202 1)\, no. 7\, 108851\, 18 pp.\n\nhttps://indico.eimi.ru/event/321/contribut ions/198/ LOCATION: URL:https://indico.eimi.ru/event/321/contributions/198/ END:VEVENT BEGIN:VEVENT SUMMARY:On Landau's type estimates for coefficients of univalent functions DTSTART;VALUE=DATE-TIME:20210702T143000Z DTEND;VALUE=DATE-TIME:20210702T145000Z DTSTAMP;VALUE=DATE-TIME:20260414T002242Z UID:indico-contribution-321-197@indico.eimi.ru DESCRIPTION:Speakers: Diana Khammatova (Kazan Federal University)\nWe esti mate the sum of coefficients for functions with restrictions on the pre-Sc hwarzian derivative. We obtained the estimate\,which is sharp up to the co nstant and found upper and lower bounds for that constant. Also we estimat ed the sum of the first three coefficients for all functions $f$\, such th at $\\log f'(z)$ is bounded with respect to the Bloch norm.\n\nhttps://ind ico.eimi.ru/event/321/contributions/197/ LOCATION: URL:https://indico.eimi.ru/event/321/contributions/197/ END:VEVENT BEGIN:VEVENT SUMMARY:High order isometric liftings and dilations DTSTART;VALUE=DATE-TIME:20210703T121500Z DTEND;VALUE=DATE-TIME:20210703T125500Z DTSTAMP;VALUE=DATE-TIME:20260414T002242Z UID:indico-contribution-321-196@indico.eimi.ru DESCRIPTION:Speakers: Vladimir Müller (Mathematical Institute\, Czech Aca demy of Sciences)\nWe show that a Hilbert space bounded linear operator ha s an m-isometric lifting for some integer $m \\ge 1$ if and only if the no rms of its powers grow polynomially.\nIn analogy with unitary dilations of contractions\, we prove that such operators also have an invertible m-iso metric dilation. Joint work with C. Badea and L. Suciu.\n\nhttps://indico. eimi.ru/event/321/contributions/196/ LOCATION: URL:https://indico.eimi.ru/event/321/contributions/196/ END:VEVENT BEGIN:VEVENT SUMMARY:Stability of spectral characteristics of boundary value problems f or $2 \\times 2$ Dirac type systems DTSTART;VALUE=DATE-TIME:20210702T140500Z DTEND;VALUE=DATE-TIME:20210702T142500Z DTSTAMP;VALUE=DATE-TIME:20260414T002242Z UID:indico-contribution-321-195@indico.eimi.ru DESCRIPTION:Speakers: Anton Lunyov (Facebook\, Inc.)\nBoundary value probl ems associated in $L^2([0\,1]\; \\mathbb{C}^2)$ with the following $2 \\ti mes 2$ Dirac type equation\n\n\\begin{equation}\n L_U(Q) y = -i B^{-1} y' + Q(x) y = \\lambda y \, \\quad\n B = \\begin{pmatrix} b_1 & 0 \\\\ 0 & b_ 2 \\end{pmatrix}\, \\quad b_1 < 0 < b_2\,\\quad\n y = {\\rm col}(y_1\, y_2 )\,\n\\end{equation}\nwith a potential matrix $Q \\in L^p([0\,1]\; \\mathb b{C}^{2 \\times 2})$\, $p \\ge 1$\, and subject to the regular boundary co nditions $Uy :=\\{U_1\, U_2\\}y=0$ has been investigated in numerous paper s. If $b_2 = -b_1 =1$ this equation is equivalent to the one dimensional D irac equation.\n\nIn this talk we present recent results concerning the st ability property under the perturbation $Q \\to \\widetilde{Q}$ of differe nt spectral characteristics of the corresponding operator $L_U(Q)$ obtaine d in our recent preprint [2]. Our approach to the spectral stability relie s on the existence of triangular transformation operators for system (1) w ith $Q \\in L^1$\, which was established in our paper [1].\n\nAssuming bou ndary conditions to be strictly regular\, let $\\Lambda_{Q} = \\{\\lambda_ {Q\,n}\\}_{n \\in \\mathbb{Z}}$ be the spectrum of $L_U(Q)$. It happens th at the mapping $Q \\to \\Lambda_Q - \\Lambda_0$ sends $L^p([0\,1]\; \\math bb{C}^{2 \\times 2})$ into the weighted space $\\ell^p(\\{(1+|n|)^{p-2}\\} )$ as well as into $\\ell^{p'}$\, $p'=p/(p-1)$. One of our main results is the Lipshitz property of this mapping on compact sets in $L^p([0\,1]\; \\ mathbb{C}^{2 \\times 2})$\, $p \\in [1\, 2]$. The proof of the inclusion i nto the weighted space $\\ell^p(\\{(1+|n|)^{p-2}\\})$ involves as an impor tant ingredient inequality that generalizes classical Hardy-Littlewood ine quality for Fourier coefficients. Similar result is proved for the eigenfu nctions of $L_U(Q)$ using the deep Carleson-Hunt theorem for ``maximal'' F ourier transform. Certain modifications of these spectral stability result s are also proved for balls in $L^p([0\,1]\; \\mathbb{C}^{2 \\times 2})$\, $p \\in [1\, 2]$.\n\n**References**\n\n[1] A.A. Lunyov and M.M. Malamud\ , *On the Riesz basis property of root vectors system for $2 \\times 2$ Di rac type operators*. J. Math. Anal. Appl. **441** (2016)\, pp. 57--103 (ar Xiv:1504.04954).\n\n[2] A.A. Lunyov and M.M. Malamud\, *Stability of spect ral characteristics and Bari basis property of boundary value problems for $2 \\times 2$ Dirac type systems*. arXiv:2012.11170.\n\nhttps://indico.ei mi.ru/event/321/contributions/195/ LOCATION: URL:https://indico.eimi.ru/event/321/contributions/195/ END:VEVENT BEGIN:VEVENT SUMMARY:On factorization of nuclear operators through $S_{s\,p}$-operators DTSTART;VALUE=DATE-TIME:20210704T074500Z DTEND;VALUE=DATE-TIME:20210704T081500Z DTSTAMP;VALUE=DATE-TIME:20260414T002242Z UID:indico-contribution-321-194@indico.eimi.ru DESCRIPTION:Speakers: Oleg Reinov ()\nWe consider the question of factoriz ations of products of $l_{r\,q}$-nuclear and close operators through the o perators of Schatten-Lorentz classes $S_{s\,p}(H).$\n\nTo get the sharpnes s of some results\, we apply the following generalization of a result of G . Pisier on convolution operators: *Given a compact Abelian group $G$ and $f\\in C(G)\,$ the convolution operator $f\\!*\\cdot: M(G) \\to C(G)$ can be factored through an $S_{s\,p}$-operator if and only if the set $\\hat f $ of Fourier coefficients of $f$ is in $l_{r\,q}\,$ where $1/q=1/p+1\, 1/r =1/s+1.$* If $q=r=1\,$ we get the result of G. Pisier.\n\nhttps://indico. eimi.ru/event/321/contributions/194/ LOCATION: URL:https://indico.eimi.ru/event/321/contributions/194/ END:VEVENT BEGIN:VEVENT SUMMARY:A dual approach to Burkholder's estimates and applications DTSTART;VALUE=DATE-TIME:20210701T093000Z DTEND;VALUE=DATE-TIME:20210701T100000Z DTSTAMP;VALUE=DATE-TIME:20260414T002242Z UID:indico-contribution-321-193@indico.eimi.ru DESCRIPTION:Speakers: Adam Osekowski (University of Warsaw)\nA celebrated result of Burkholder from the 80's identifies the best constant in the $L^ p$ estimate for martingale transforms ($1 < p < \\infty$). This result is a starting point for numerous extensions and applications in many areas of mathematics. Burkholder's proof exploits the so-called Bellman function m ethod: it rests on the construction of a certain special function\, enjoyi ng appropriate size and concavity requirements. This special function is o f interest on its own right and appears\, quite unexpectedly\, in the cont ext of quasiconformal mappings and geometric function theory. There is a d ual approach to the $L^p$ bound\, invented by Nazarov\, Treil and Volberg in the 90's. It gives a slightly worse constant\, but the alternative Bell man function plays an independent\, significant role in harmonic analysis\ , as evidenced in many papers in the last 20 years. \n\nThe purpose of the talk is to show how to improve the latter approach so that it produces th e best constant and to discuss a number of applications.\n\nhttps://indico .eimi.ru/event/321/contributions/193/ LOCATION: URL:https://indico.eimi.ru/event/321/contributions/193/ END:VEVENT BEGIN:VEVENT SUMMARY:Properties of spectra of differentiation invariant subspace in the Schwarz space DTSTART;VALUE=DATE-TIME:20210702T074500Z DTEND;VALUE=DATE-TIME:20210702T081500Z DTSTAMP;VALUE=DATE-TIME:20260414T002242Z UID:indico-contribution-321-192@indico.eimi.ru DESCRIPTION:Speakers: Natalia Abuzyarova (Bashkir State University)\nLet $ E$ be the Schwartz space of infinitely differentiable functions on the rea l line. We consider its closed differentiation invariant subspace $W$ with discrete spectrum $L$ which is weakly synthesable. It means that $W$ is t he closed span of its residual subspace and the set $\\rm{Exp} W$ of all exponential monomials contained in $W$. Among all weakly synthesable subsp aces $W$\, there are nice ones which equal the direct (algebraical and top ological) sum of the residual part of $W$ and the closed span of $\\rm{Exp } W$. Does given weakly synthesable subspace $W$ equal such a direct sum o r not? The answer is obtained in terms of characteristics and (or) propert ies of the spectrum $L$.\n\nhttps://indico.eimi.ru/event/321/contributions /192/ LOCATION: URL:https://indico.eimi.ru/event/321/contributions/192/ END:VEVENT BEGIN:VEVENT SUMMARY:The Nevanlinna characteristic and integral inequalities with maxim al radial characteristic for meromorphic functions and differences of subh armonic functions DTSTART;VALUE=DATE-TIME:20210704T070000Z DTEND;VALUE=DATE-TIME:20210704T074000Z DTSTAMP;VALUE=DATE-TIME:20260414T002242Z UID:indico-contribution-321-191@indico.eimi.ru DESCRIPTION:Speakers: Bulat Khabibullin (Bashkir State University)\nLet $f $ be a meromorphic function on the complex plane $\\mathbb C$ with the max imum function of its modulus $M(r\,f)$ on circles centered at zero of radi us $r$. A number of classical\, well-known and widely used results allow u s to estimate from above the integrals of the positive part of the logarit hm ln M(t\,f) over subsets of $E\\subset [0\,r]$ via the Nevanlinna charac teristic T(r\,f) and the linear Lebesgue measure of the set $E$. We give m uch more general estimates for the Lebesgue-Stieltjes integrals of $ln^+M( t\,f)$ over the increasing integration function of $m$. Our results are es tablished immediately for the differences of subharmonic functions on clos ed circles centered at zero\, i.e.\, $ \\delta $ -subharmonic functions\, but they are new for meromorphic functions on $\\mathbb C$ and contain all the previous results on this topic as a very special and extreme case. Th e only condition in our main theorem is the Dini condition for the modulus of continuity of the integration function $m$. This condition is\, in a s ense\, necessary. Thus\, our results\, to a certain extent\, complete stud y upper estimates of the integrals of the radial maximum growth characteri stics of arbitrary meromorphic and $\\delta$-subharmonic functions through the Nevanlinna characteristic with its versions and through quantities a ssociated with the integration function $m$ such as the Hausdorff $h$-mea sure or $h$-content\, and the $d$-dimensional Hausdorff measure of the sup port of nonconstancy for $m$.\n\nhttps://indico.eimi.ru/event/321/contribu tions/191/ LOCATION: URL:https://indico.eimi.ru/event/321/contributions/191/ END:VEVENT BEGIN:VEVENT SUMMARY:Discrete temperate distributions in Euclidean spaces DTSTART;VALUE=DATE-TIME:20210703T135500Z DTEND;VALUE=DATE-TIME:20210703T142500Z DTSTAMP;VALUE=DATE-TIME:20260414T002242Z UID:indico-contribution-321-190@indico.eimi.ru DESCRIPTION:Speakers: Sergii Favorov (Karazin's Kharkiv national universit y)\nLet $f=\\sum_{\\lambda\\in\\Lambda}\\sum_k p_k(\\lambda) D^k\\delta_\ \lambda$ be a temperate distribution on $\\mathbb{R}^d$ with uniformly dis crete support $\\Lambda$ and uniformly discrete spectrum (that is $supp\\h at f$). We prove that under conditions\n$$\n 0 < c\\le\\sum_k|p_k(\\lam bda)|\\le C < \\infty\n$$\nthe support $\\Lambda$ is a finite union of cos ets of full-rank lattices. The optimality of the above estimates is discus sed. The result generalizes the corresponding one for discrete measures [1 ]. For its proof we use some properties of almost periodic distributions a nd a local version of Wiener's Theorem on trigonometric series.\n\n[1] S. Yu.Favorov\, *Large Fourier Quasicrystals and Wiener's Theorem*\, Journal of Fourier Analysis and Applications\, Vol. 25\, Issue 2\, (2019)\, 377-3 92.\n\nhttps://indico.eimi.ru/event/321/contributions/190/ LOCATION: URL:https://indico.eimi.ru/event/321/contributions/190/ END:VEVENT BEGIN:VEVENT SUMMARY:Inequalities for hypercubic functionals. Generalized Chebyshev ine qualities. DTSTART;VALUE=DATE-TIME:20210704T131500Z DTEND;VALUE=DATE-TIME:20210704T133500Z DTSTAMP;VALUE=DATE-TIME:20260414T002242Z UID:indico-contribution-321-189@indico.eimi.ru DESCRIPTION:Speakers: Armenak Gasparyan ()\nBy hypercubic functionals we m ean expressions of type\n$$\nG_p{}^{(\\sigma)}(\\Phi\,F) =\\sum _{k \\in B _2^p} (-1)^{(\\sigma\,\nk)}\\Phi (k\,F)\\\,\\Phi (\\overline{k}\,F)\n$$\nw here $\\sigma \\in B_2^p =\\{0\,1\\}^p$\,\\\, $\\Phi :\\\,\nB_2^p\\times { \\cal F} \\to R(or\\\, C)$\, and ${\\cal F}\\subseteq V^p$\, $V$\n--- some functional space.\nIn very particular case $p=2$\, this family of functio nals contains\nBinet-Cauchy\, Chebyshev\, Cauchy-Bunyakovsky-Schwarz\, New ton\,\nAlexandrov and some other type functionals for which there hold wel l\nknown identities and inequalities.\nBy this talk\, I think to familiari ze colleagues with identities and\ninequalities established for abovedefin ed hypercubic functionals.\nSome applications also will be discussed.\n\nh ttps://indico.eimi.ru/event/321/contributions/189/ LOCATION: URL:https://indico.eimi.ru/event/321/contributions/189/ END:VEVENT BEGIN:VEVENT SUMMARY:Trace and extension theorems for Sobolev $W^{1}_{p}(\\mathbb{R}^{n })$-spaces. The case $p \\in (1\,n]$. DTSTART;VALUE=DATE-TIME:20210706T074500Z DTEND;VALUE=DATE-TIME:20210706T081500Z DTSTAMP;VALUE=DATE-TIME:20260414T002242Z UID:indico-contribution-321-188@indico.eimi.ru DESCRIPTION:Speakers: Alexander Tyulenev (Steklov Mathematical Institute o f RAS)\nLet $S \\subset \\mathbb{R}^{n}$ be an arbitrary nonempty compact set such that the $d$-Hausdorff content $\\mathcal{H}^{d}_{\\infty}(S) > 0 $ for some $d \\in (0\,n]$. For each $p \\in (\\max\\{1\,n-d\\}\,n]$ we g ive an almost sharp intrinsic description of the trace space $W_{p}^{1}(\\ mathbb{R}^{n})|_{S}$ of the Sobolev space $W_{p}^{1}(\\mathbb{R}^{n})$. Fu rthermore\, for each$\\varepsilon \\in (0\, \\min\\{p-(n-d)\,p-1\\})$ we c onstruct a new bounded linear extension operator $\\mathrm{Ext}_{S\,d\,\\v arepsilon}$ mapping the trace space $W_{p}^{1}(\\mathbb{R}^{n})|_{S}$ to the space $W_{p-\\varepsilon}^{1}(\\mathbb{R}^{n})$ such that $\\mathrm{Ex t}_{S\,d\,\\varepsilon}$ is a right inverse operator for the corresponding trace operator. The construction of the operator $\\mathrm{Ext}_{S\,d\,\\ varepsilon}$ does not depend on $p$ and based on new delicate combinatoria l methods.\n\nhttps://indico.eimi.ru/event/321/contributions/188/ LOCATION: URL:https://indico.eimi.ru/event/321/contributions/188/ END:VEVENT BEGIN:VEVENT SUMMARY:Hölder regularity of solutions to a non-local drift-diffusion equ ation\, along a non-solenoidal BMO flow DTSTART;VALUE=DATE-TIME:20210704T125000Z DTEND;VALUE=DATE-TIME:20210704T131000Z DTSTAMP;VALUE=DATE-TIME:20260414T002242Z UID:indico-contribution-321-186@indico.eimi.ru DESCRIPTION:Speakers: Ioann Vasilyev (Universite Paris Saclay)\nIn this ta lk\, we shall show how to apply methods of the real harmonic analysis in o rder to prove the critical Hölder regularity of solutions to a critical n on-local transport-diffusion equation\, in case when the velocity field is in BMO and is not necessarily divergence free. Our proofs are inspired by some ideas of F. Nazarov and A. Kiselev. The talk is based on a recent jo int work with F. Vigneron.\n\nhttps://indico.eimi.ru/event/321/contributio ns/186/ LOCATION: URL:https://indico.eimi.ru/event/321/contributions/186/ END:VEVENT BEGIN:VEVENT SUMMARY:Nonlinear elliptic equations with subcoercive operators DTSTART;VALUE=DATE-TIME:20210704T144500Z DTEND;VALUE=DATE-TIME:20210704T150500Z DTSTAMP;VALUE=DATE-TIME:20260414T002242Z UID:indico-contribution-321-185@indico.eimi.ru DESCRIPTION:Speakers: Eugene Kalita ()\nLet $X\, Y$ be separable reflexive Banach spaces\, $X\\subset Y$ densely.\nLet $A: X\\to X^*$ be monotone op erator (dissipative\, in linear case)\, \ncoercive in the norm of $Y$\, th at is $(Au\,u)/\\|u\\|_Y \\to \\infty$ as $\\|u\\|_Y \\to \\infty\, \\ u\\ in X$.\n\nWe introduce a notion of solution of equation $Au=f$ for $u\\in Y$\, $f\\in Y^*$ in such the situation. \nIn case $\\exists\\\,V\\subset X $ dense (and so $V\\subset Y$ dense) with $Av\\in Y^*$ for $v\\in V$\, \no ur solution coincides with the solution in sense of monotonic extension of operator $A$.\n\nWe treat elliptic equations of nonstrictly divergent for m \n${\\rm{div}}^t A(x\,D^su)=f(x)$\, $s\\ne t$\, $x\\in R^n$\, \nunder de generate Cordes-type condition \nand achieve existence and uniqueness resu lts \nin wider situation than already known.\n\nhttps://indico.eimi.ru/eve nt/321/contributions/185/ LOCATION: URL:https://indico.eimi.ru/event/321/contributions/185/ END:VEVENT BEGIN:VEVENT SUMMARY:Weighted Hardy-Hilbert spaces of analytic functions and their comp osition operators DTSTART;VALUE=DATE-TIME:20210702T084000Z DTEND;VALUE=DATE-TIME:20210702T092000Z DTSTAMP;VALUE=DATE-TIME:20260414T002242Z UID:indico-contribution-321-184@indico.eimi.ru DESCRIPTION:Speakers: Hervé Queffélec (University of Lille)\nLet $\\math bb{D}$ be the unit disk and $\\beta=(\\beta_n)_{n\\geq 0}$ a sequence of positive numbers satisfying $$\\liminf_{n\\to \\infty} \\beta_{n}^{1/n}\\g eq 1.$$ The associated Hardy space $H=H^{2}(\\beta)\\subset \\mathcal{H}(\ \mathbb{D})$ is the set of analytic functions $f(z)=\\sum_{n=0}^\\infty a_ n z^n$ such that\n$$\\Vert f\\Vert^2=\\sum_{n=0}^\\infty|a_n|^2 \\beta_n\n \nhttps://indico.eimi.ru/event/321/contributions/184/ LOCATION: URL:https://indico.eimi.ru/event/321/contributions/184/ END:VEVENT BEGIN:VEVENT SUMMARY:An infinite product of extremal multipliers of a Hilbert space wit h Schwarz-Pick kernel DTSTART;VALUE=DATE-TIME:20210702T145500Z DTEND;VALUE=DATE-TIME:20210702T151500Z DTSTAMP;VALUE=DATE-TIME:20260414T002242Z UID:indico-contribution-321-183@indico.eimi.ru DESCRIPTION:Speakers: Ilya Videnskii (St. Petersburg State University)\nFo r a reproducing kernel Hilbert space $H$ on a set $X$ we define a distance $d(a\,Z)$ between a point $a$ and a subset $Z$. A space $H$ has the Schwa rz-Pick kernel if for every pair $(a\,Z)$ there exists an extremal multipl ier of norm less or equal than one\, which vanishes at the set $Z$ and at tains the value $d(a\,Z)$ at the point $a$. For a normalized Hilbert space with Schwarz-Pick kernel and for a sequence of subsets that satisfies an abstract Blaschke condition we prove that the associate Blaschke product o f extremal multipliers converges in the norm of $H$.\n\nhttps://indico.eim i.ru/event/321/contributions/183/ LOCATION: URL:https://indico.eimi.ru/event/321/contributions/183/ END:VEVENT BEGIN:VEVENT SUMMARY:Hardy's inequalities for the Jacobi weight DTSTART;VALUE=DATE-TIME:20210704T122500Z DTEND;VALUE=DATE-TIME:20210704T124500Z DTSTAMP;VALUE=DATE-TIME:20260414T002242Z UID:indico-contribution-321-182@indico.eimi.ru DESCRIPTION:Speakers: Ramil Nasibullin (Kazan Federal University)\nWe prov e onedimensional new Hardy type inequalities for Jacoby eights. Using this inequality\, we obtain Nehari-Pokornii type univalence conditions for a nalytic in the unite disk $\\mathbb{D}=\\{z\\in\\mathbb{C}: |z|<1\\}$ func tions. The following theorem holds.\n\nTheorem 1. Suppose that $f$ is mero morphic in $\\mathbb{D}$ function. If $n\\in \\mathbb{N}$\, $a_k$ and $\\m u_k$\, $k=\\overline{1\,n}$\, are positive real numbers and\n$$\n|S_f(z)| \\leq \\sum_{k=1}^n \\frac{b_k A(\\mu_k)}{(1-|z|^2)^{\\mu_k}}\, \\quad z\\ in \\mathbb{D}\,\n$$\nwhere $b_k=\\frac{2P_{2-\\mu_k}}{A(\\mu_k)} \\ a_k$\ , $a_1+a_2+ \\ldots + a_n\\leq 1$\, $0\\leq \\mu_1\\leq \\mu_2\\leq \\ldot s \\leq \\mu_n\\leq 2$ and\n$$\nA(\\mu)=\n\\begin{cases}\n2^{3\\mu-1}\\pi^ {2(1-\\mu)}\, & 0\\leq \\mu \\leq 1\, \\\\\n2^{3-\\mu}\, & 1\\leq \\mu \\l eq 2\;\n\\end{cases}\n$$\nThen the function $f$ is univalent in $\\mathbb{ D}$.\n\nhttps://indico.eimi.ru/event/321/contributions/182/ LOCATION: URL:https://indico.eimi.ru/event/321/contributions/182/ END:VEVENT BEGIN:VEVENT SUMMARY:Complex symmetric operators and inverse spectral problem for Hanke l operators DTSTART;VALUE=DATE-TIME:20210701T070500Z DTEND;VALUE=DATE-TIME:20210701T074500Z DTSTAMP;VALUE=DATE-TIME:20260414T002242Z UID:indico-contribution-321-181@indico.eimi.ru DESCRIPTION:Speakers: Sergei Treil (Brown University)\nHankel operators ar e bounded operators on $\\ell^{2}$ whose matrix is constant on diagonals o rthogonal to the main one (i.e. its entries depend only on the sum of indi ces). Such operators connect many classical problems in complex analysis w ith problems in operator theory.\n\nI’ll be discussing the inverse spect ral problem for such operators\, i.e. the problem of finding a Hankel oper ator with prescribed spectral data. For non-selfadjoint operators the theo ry of the so-called *complex symmetric* operators gives a convenient way t o present such spectral data.\n\nIt was discovered by P. Gerard and S. Gre llier that the spectral data of a compact Hankel operator $\\Gamma$ and t he reduced Hankel operator $\\Gamma S$ (where $S$ is the forward shift in $\\ell^2$) completely determine the Hankel operator $\\Gamma$. This turns out to be the case for general Hankel operators as well\, i.e. the map fr om Hankel operators to the spectral data of $\\Gamma$ and of $\\Gamma S$ i s injective. But what about surjectivity?\n\nIn the talk I'll discuss some positive results\, as well as some counterexamples. Connections with Clar k measures play an important role in the investigation\, and will be discu ssed.\n\nThe talk is based on a joint work with P. Gerard and A. Pushni tskii.\n\nhttps://indico.eimi.ru/event/321/contributions/181/ LOCATION: URL:https://indico.eimi.ru/event/321/contributions/181/ END:VEVENT BEGIN:VEVENT SUMMARY:A canonical system related to the Riemann zeta function DTSTART;VALUE=DATE-TIME:20210706T095000Z DTEND;VALUE=DATE-TIME:20210706T101000Z DTSTAMP;VALUE=DATE-TIME:20260414T002242Z UID:indico-contribution-321-180@indico.eimi.ru DESCRIPTION:Speakers: Vladimir Kapustin (St. Petersburg Department of Stek lov Mathematical Institute)\nWe present a de Branges space and the associa ted canonical system related to the Riemann zeta function.\n\nhttps://indi co.eimi.ru/event/321/contributions/180/ LOCATION: URL:https://indico.eimi.ru/event/321/contributions/180/ END:VEVENT END:VCALENDAR