BEGIN:VCALENDAR VERSION:2.0 PRODID:-//CERN//INDICO//EN BEGIN:VEVENT SUMMARY:Spectral invariants of circulant graphs and their application in c ombinatorial analysis DTSTART;VALUE=DATE-TIME:20230705T090000Z DTEND;VALUE=DATE-TIME:20230705T094500Z DTSTAMP;VALUE=DATE-TIME:20260807T110330Z UID:indico-contribution-1238-550@indico.eimi.ru DESCRIPTION:Speakers: Alexander Mednykh ()\nThe purpose of this report is to study the spectral invariants of circulant graphs and their generalizat ions. Circulant graphs arise as cyclic coverings of a single-vertex graph with a given number of loops. More complex representatives of the family o f cyclic coverings are I-\, Y-\, H-graphs\, generalized Petersen graphs\, sandwich graphs\, discrete tori\, and many others.\n\nIn the talk\, analyt ical formulas will be given that allow one to calculate the number of root ed spanning forests and trees in cyclic coverings\, their asymptotics will be found\, and the arithmetic properties of these numbers will be studied . In addition\, for circulant graphs\, exact formulas for calculating the Kirchhoff index will be indicated and it will be established that\, up to an exponentially small remainder term\, they are given by polynomials of t he third degree.\n\nAll these quantities are spectral invariants. They dep end on the eigenvalues of the characteristic polynomial of the Laplace mat rix. The structure of the polynomial itself for circulant graphs remained unknown. In recent papers [Xiaogang Liu and Sanming Zhou (2012)\, Xiaogang Liu and Pengli Lu (2016)]\, it was found that the characteristic polynomi als for a number of well-known families of graphs\, such as the theta grap h\, dumbbell graph\, and propeller graph\, are effectively expressed in te rms of Chebyshev polynomials. These results gave the key to understanding the structure of the characteristic polynomial for circulant graphs. \n\n We will show that the characteristic polynomial can be represented as a fi nite product of algebraic functions calculated in the roots of a linear co mbination of Chebyshev polynomials. In particular\, this will make it poss ible to establish the periodicity of such polynomials at prescribed intege r points\, which is of interest from the point of view of discrete topolog ical dynamics. \n\nReferences\n \n[1] A.D. Mednykh\, I.A. Mednykh\, Cyclic coverings of graphs. Enumeration of rooted spanning forests and trees\, K irchhoff index and Jacobians. Uspehi matematiheskikh nauk\, 2023\, Vol. 78 \, Is. 3(471)\, p. 115-160.\n\nhttps://indico.eimi.ru/event/1238/contribut ions/550/ LOCATION: URL:https://indico.eimi.ru/event/1238/contributions/550/ END:VEVENT BEGIN:VEVENT SUMMARY:Uniform approximation by polynomial solutions of certain elliptic PDE and systems DTSTART;VALUE=DATE-TIME:20230701T090000Z DTEND;VALUE=DATE-TIME:20230701T094500Z DTSTAMP;VALUE=DATE-TIME:20260807T110330Z UID:indico-contribution-1238-536@indico.eimi.ru DESCRIPTION:Speakers: Konstantin Fedorovskiy (Lomonosov Moscow State Unive rsity)\nWe plan to discuss the problems on uniform approximation of functi ons on compact sets in the complex plane by elements of polynomial modules of polyanalytic type generated by antiholomorphic functions and by polyno mial solutions to general second-order elliptic but not strongly elliptic systems\nof PDEs with constant coefficients. We will present some known an d recent results in this topis and explore the special analytic characteri stics of planar simply connected domains in terms of which the obtained ap proximation criteria are stated (the concept of a $g$-Nevanlinna domain\, where $g$ is the\ngenerator of the module by elements of which the approxi mation is carried out\, and\, the concept of an $L$-special domain\, where $L$ is the elliptic differential operator that determines the correspondi ng system).\n\nThe talk is based on the results obtained in frameworks of the project 22--11--00071 by the Russian Science Foundation.\n\nhttps://in dico.eimi.ru/event/1238/contributions/536/ LOCATION: URL:https://indico.eimi.ru/event/1238/contributions/536/ END:VEVENT BEGIN:VEVENT SUMMARY:Lattice equations and semiclassical asymptotics DTSTART;VALUE=DATE-TIME:20230704T070000Z DTEND;VALUE=DATE-TIME:20230704T074500Z DTSTAMP;VALUE=DATE-TIME:20260807T110330Z UID:indico-contribution-1238-551@indico.eimi.ru DESCRIPTION:Speakers: Vladimir Nazaikinskii (Institute for Problems in Mec hanics RAS\, Moscow)\nWe consider linear equations with shifts of the argu ments on the rectangular lattice with small step $h$ in $\\mathbb{R}^n$ an d construct a version of the canonical operator providing semiclassical as ymptotics for such equations. In the case of functions of continuous argum ent\, equations with shifts can be written as $h$-pseudodifferential equat ions with symbols $2\\pi$-periodic in the momenta. This representation can also be given meaning for functions of a discrete argument\, although dif ferentiation operators are not defined for lattice functions. The phase sp ace of such equations is the product $\\mathbb{R}^n\\times T^n$. Developin g Maslov's ideas\, we construct a canonical operator on Lagrangian submani folds of this phase space with values in the space of lattice functions. C ompared with the classical version of the canonical operator and the new f ormulas recently introduced by S.Yu.Dobrokhotov\, A.I.Shafarevich\, and th e author\, the construction involves a number of new features.\n\nAs an ex ample\, we give equations on a two-dimensional lattice that arise in quant um theory (the Feynman checkers model) and in the problem on the propagati on of wave packets on a homogeneous tree.\n\nThe talk is based on the resu lts of joint work with V.L.Chernyshev (HSE University\, Moscow) and A.V.Ts vetkova (Ishlinsky Institute for Problems in Mechanics RAS\, Moscow). The author's research was supported by the Russian Foundation for Basic Resear ch under project no. 21-51-12006.\n\nhttps://indico.eimi.ru/event/1238/con tributions/551/ LOCATION: URL:https://indico.eimi.ru/event/1238/contributions/551/ END:VEVENT BEGIN:VEVENT SUMMARY:Regularized sums for eigenvalues of bounded perturbations of model second-order partial derivative operators DTSTART;VALUE=DATE-TIME:20230702T113000Z DTEND;VALUE=DATE-TIME:20230702T121500Z DTSTAMP;VALUE=DATE-TIME:20260807T110330Z UID:indico-contribution-1238-549@indico.eimi.ru DESCRIPTION:Speakers: Ziganur Fazullin (Ufa University of Science and Tech nology)\nWe are going to discuss problems and analyze calculation of regul arized trace formulas for perturbed model second-order partial derivative operators if the perturbation is performed by the operator of multiplicati on by function. In particular\, we will formulate certain results on the q uestion for Laplace-Beltrami operator on $S^2$\, for harmonic oscillator a cting in the whole plane $\\mathbb R^2$ or in a strip\, for Schr\\”oding er operator in homogeneous magnetic field. We will also discuss certain ap proaches and results for Dirichlet problem on a square\n\nhttps://indico.e imi.ru/event/1238/contributions/549/ LOCATION: URL:https://indico.eimi.ru/event/1238/contributions/549/ END:VEVENT BEGIN:VEVENT SUMMARY:"Good" multipliers in higher dimensions DTSTART;VALUE=DATE-TIME:20230704T133000Z DTEND;VALUE=DATE-TIME:20230704T141000Z DTSTAMP;VALUE=DATE-TIME:20260807T110330Z UID:indico-contribution-1238-548@indico.eimi.ru DESCRIPTION:Speakers: Ioann Vasilyev (Université Paris-Saclay)\nIn this t alk\, we shall show how to construct "good" Fourier multipliers in higher dimensions. If time permits\, we shall also show how to apply these multip liers to some modern problems of the uncertainty principle in harmonic ana lysis.\n\nhttps://indico.eimi.ru/event/1238/contributions/548/ LOCATION: URL:https://indico.eimi.ru/event/1238/contributions/548/ END:VEVENT BEGIN:VEVENT SUMMARY:Weighted Bernstein's inequality in $L^p$ on the axis with power we ight for $p > 0$ DTSTART;VALUE=DATE-TIME:20230704T141500Z DTEND;VALUE=DATE-TIME:20230704T145500Z DTSTAMP;VALUE=DATE-TIME:20260807T110330Z UID:indico-contribution-1238-547@indico.eimi.ru DESCRIPTION:Speakers: Dmitry Gorbachev (Tula State University)\nBernstein' s inequality for the derivative of a trigonometric polynomial in the $L^p$ space is a classical inequality of approximation theory. It has been gene ralized to the case of entire functions of exponential type on the axis. T he question of\nboundedness of the constant remained open in the case of a power weight for $p > 0$. We show that this is true for both the ordinary derivative and the Dunkl differential-difference operator.\n\nhttps://ind ico.eimi.ru/event/1238/contributions/547/ LOCATION: URL:https://indico.eimi.ru/event/1238/contributions/547/ END:VEVENT BEGIN:VEVENT SUMMARY:Calderón-Mityagin and Arazy-Cwikel type interpolation properties for quasi-Banach spaces DTSTART;VALUE=DATE-TIME:20230706T081000Z DTEND;VALUE=DATE-TIME:20230706T085500Z DTSTAMP;VALUE=DATE-TIME:20260807T110330Z UID:indico-contribution-1238-544@indico.eimi.ru DESCRIPTION:Speakers: Sergei Astashkin (Samara National Research Universit y)\nWe plan to discuss some recent results (see [1-3]) related to Calderó n-Mityagin and Arazy-Cwikel interpolation properties in the class of quasi -Banach spaces. As an example\, we will consider the classical family of c ouples $(\\ell^{p}\,\\ell^{q})$\, $0 \\le p < q \\le \\infty$\, focusing o n an identification of interpolation orbits of elements with respect to su ch a couple for any $p$ and $q$\, $0 \\le p\n\nhttps://indico.eimi.ru/even t/1238/contributions/544/ LOCATION: URL:https://indico.eimi.ru/event/1238/contributions/544/ END:VEVENT BEGIN:VEVENT SUMMARY:Hypercubic generalizations and refinements of Cauchy-Bunyakovsky-S chwarz inequality DTSTART;VALUE=DATE-TIME:20230702T142500Z DTEND;VALUE=DATE-TIME:20230702T145500Z DTSTAMP;VALUE=DATE-TIME:20260807T110330Z UID:indico-contribution-1238-546@indico.eimi.ru DESCRIPTION:Speakers: Armenak Gasparyan (Ailamazyan Program Systems Instit ute of Russian Academy of Sciences)\nThe classical Cauchy-Bunyakovsky-Schw arz inequality is one of fundamental inequalities of mathematics that have been generalized and applied by many mathematicians in different directio ns. In the talk a family of new type generalizations are presented for CBS inequality. These results are applied to give infinite sequence of refine ments both of same CBS inequality and its generalizations.\n\nhttps://indi co.eimi.ru/event/1238/contributions/546/ LOCATION: URL:https://indico.eimi.ru/event/1238/contributions/546/ END:VEVENT BEGIN:VEVENT SUMMARY:Gaussian multiplicative chaos and excess one for the sine-process DTSTART;VALUE=DATE-TIME:20230702T081000Z DTEND;VALUE=DATE-TIME:20230702T085500Z DTSTAMP;VALUE=DATE-TIME:20260807T110330Z UID:indico-contribution-1238-545@indico.eimi.ru DESCRIPTION:Speakers: Alexander Bufetov (Steklov Mathematical Institute of Russian Academy of Sciences)\nThe main result of the talk is that the ran dom entire function \nassociated to the sine-process converges to the Gaus sian multiplicative chaos under suitable normalization. As a corollary of the developed formalism\, we obtain that almost every realization of the sine-process\, after removing one particle\, becomes a complete minimal se t for the Paley-Wiener space.\n\nhttps://indico.eimi.ru/event/1238/contrib utions/545/ LOCATION: URL:https://indico.eimi.ru/event/1238/contributions/545/ END:VEVENT BEGIN:VEVENT SUMMARY:Real-valued spectral shift functions for pairs of contractions and pairs of dissipative operators DTSTART;VALUE=DATE-TIME:20230701T113000Z DTEND;VALUE=DATE-TIME:20230701T121500Z DTSTAMP;VALUE=DATE-TIME:20260807T110330Z UID:indico-contribution-1238-543@indico.eimi.ru DESCRIPTION:Speakers: Vladimir Peller (St.Petersburg StateUniversity)\nThe talk is based on joint results with M.M. Malamud. I am going to discuss c onditions under which a pair of contractions on Hilbert space with trace c lass difference has a real integrable spectral shift functions. The case o f pairs of dissipative operators will also be discussed.\n\nThe work is su pported by the Ministry of Education and Science of the Russian Federation within the framework of the state task (project number FSSF-2023-0016).\n \nhttps://indico.eimi.ru/event/1238/contributions/543/ LOCATION: URL:https://indico.eimi.ru/event/1238/contributions/543/ END:VEVENT BEGIN:VEVENT SUMMARY:On a formula for characteristic determinants of boundary value pro blems for $n \\times n$ Dirac type equations and its applications DTSTART;VALUE=DATE-TIME:20230704T124500Z DTEND;VALUE=DATE-TIME:20230704T132500Z DTSTAMP;VALUE=DATE-TIME:20260807T110330Z UID:indico-contribution-1238-542@indico.eimi.ru DESCRIPTION:Speakers: Mark Malamud (Peoples Friendship University of Russi a (RUDN University))\nIn this talk it will be discussed spectral properti es of boundary value problems for the following first order system of or dinary differential equations \n\\begin{equation*} %\\label{eq:Ly.abstract }\n L y = -i B(x)^{-1} \\bigl(y' + Q(x) y\\bigr) = \\lambda y \, \\quad\n B(x) = B(x)^*\, \\quad y= {\\rm co}l(y_1\, \\ldots\, y_n)\, \\quad x \\in [0\,\\ell]\,\n\\end{equation*}\non a finite interval $[0\,\\ell]$. Here $Q \\in L^1([0\,\\ell]\; \\bC^{n \\times n})$ is a potential matrix and $B \ \in L^{\\infty}([0\,\\ell]\; \\bR^{n \\times n})$ is an invertible self-ad joint diagonal ``weight'' matrix. If $n=2m$ and $B(x) = {\\rm diag}(-I_m\, I_m)$ this equation is equivalent to the classical Dirac equation of orde r $n$. We will discuss the spectral properties of boundary value problem s associated with the above equation subject to general boundary conditi ons $U(y)=Cy(0)+Dy(\\ell) = 0$ satisfying the maximality condition ${\\r m rank}(C \\ D) = n$.\n\nOne of our main results is the formula for the deviation of the characteristic determinants $\\Delta(\\lambda) - \\Delta_ 0(\\lambda)$ of the perturbed and unperturbed (with $Q=0$) boundary va lue problems subject to the same boundary conditions $U(y) = 0$. Namely it is shown that it is a Fourier transform of a certain integrable function explicitly expressed via kernels of the transformation operators.\n\n In turn\, this result is applied to establish asymptotic behavior of eigenva lues as well as sharp evaluation of the reminder.\n\nJoint work with Ant on Lunyov.\n\nhttps://indico.eimi.ru/event/1238/contributions/542/ LOCATION: URL:https://indico.eimi.ru/event/1238/contributions/542/ END:VEVENT BEGIN:VEVENT SUMMARY:Generalizations of Rellich and Birman integral inequalities DTSTART;VALUE=DATE-TIME:20230704T120000Z DTEND;VALUE=DATE-TIME:20230704T124000Z DTSTAMP;VALUE=DATE-TIME:20260807T110330Z UID:indico-contribution-1238-541@indico.eimi.ru DESCRIPTION:Speakers: Farit Avkhadiev (Kazan Federal University)\nWe cons ider integral inequalities for functions $f\\in C_0^{\\infty}(\\Omega)$ on domains $\\Omega$ of the Euclidean space $\\mathbb{R}^n$\, $n\\in \\math bb{N}$.\n There are several inequalities connected with two following bas ic results. Namely\, in 1954 F. Rellich proved that\n$$\n\\int_{\\mathbb{R }^n} |\\Delta f|^2 \\\,dx\\geq\n\\frac{n^2(n-4)^2}{16}\\int_{\\mathbb{R}^n }\\frac{|f|^2} {|x|^{4}} dx\, \\quad \\quad\n \\forall f\\in C_0^\\infty(\ \mathbb{R}^n\\setminus \\{0\\}) \\\,\\\, (n\\geq 3)\,\n$$\nwhere $\\Delt a f$ is the Laplacian of the function $f:\\mathbb{R}^n\\setminus \\{0\\ } \\to\\mathrm{C}$.\n\nIn 1961 M. Sh. Birman proved that\n $$\n \\int_0^ {\\infty}|f^{(k)}(t)|^2 dt \\geq \\left(\n\\frac{(2k-1)!!}{2^k} \\right)^ 2\\int_0^{\\infty}\\frac{|f(t)|^2}{t^{2k}} dt\, \\quad \\forall f \\in C_ 0^\\infty(0\, \\infty)\\\,\\\, (k\\in \\mathbb{N}).\n $$\n We will describ e direct generalizations of the Rellich and Birman inequalities. In addit ion\, using the polyharmonic operator defined by\n$$\n\\Delta^{k/2}f(x):= \\begin {cases}\n\\Delta^j f(x)\,&\\text{if $k=2j$}\,\\\\\n\\nabla \\Delt a^{j-1} f(x)\,&\\text{if $k=2j-1$}\,\n\\end {cases}\n$$\nwhere $j\\in \\ma thbb{N}$\, $k\\in \\mathbb{N}$\, $f\\in C_0^{\\infty}(\\Omega)$\, $\\Ome ga\\subset\\mathbb{R}^n$\, we describe results about the inequality\n$$\n \\int_{\\Omega} |\\Delta^{k/2} f(x)|^2 dx\\geq\nA_k(\\Omega)\\int_{\\Omeg a}\\frac{|f(x)|^2}{{\\rm dist}^{2k}(x\, \\partial\\Omega)}dx\, \\quad \\f orall f\\in C_0^\\infty(\\Omega).\n$$\n\nhttps://indico.eimi.ru/event/1238 /contributions/541/ LOCATION: URL:https://indico.eimi.ru/event/1238/contributions/541/ END:VEVENT BEGIN:VEVENT SUMMARY:Hypergeometry in the theory of algebraic functions DTSTART;VALUE=DATE-TIME:20230706T070000Z DTEND;VALUE=DATE-TIME:20230706T074500Z DTSTAMP;VALUE=DATE-TIME:20260807T110330Z UID:indico-contribution-1238-540@indico.eimi.ru DESCRIPTION:Speakers: Avgust Tsikh (Siberian Federal University)\nWe will discuss universal algebraic functions\, i.e.\, polynomial equations (or sy stems of such equations) with independent variable coefficients. It is kno wn that for such equations the algebraic functions have hypergeometric typ e (Mellin 1921\, Birkeland 1927\, Stepanenko 2015).\n\nFor functions of hy pergeometric type\, we prove an anlogue of Gorn-Kapranov theorem (1889-199 1) that states that the singularities of such functions coincide with the discriminant sets of the corresponding systems. The results obtained make it possible to calculate the convergence domains for series of hypergeomet ric type in the language of functional inequalities for modules of variabl es of power series. Existence of such inequalities can be interpreted as an appearance of "quantum entanglement" in the theory of hypergeometric st ructures of Feynman integrals.\n\nhttps://indico.eimi.ru/event/1238/contri butions/540/ LOCATION: URL:https://indico.eimi.ru/event/1238/contributions/540/ END:VEVENT BEGIN:VEVENT SUMMARY:On Gelfand-Shilov type spaces DTSTART;VALUE=DATE-TIME:20230702T070000Z DTEND;VALUE=DATE-TIME:20230702T074500Z DTSTAMP;VALUE=DATE-TIME:20260807T110330Z UID:indico-contribution-1238-539@indico.eimi.ru DESCRIPTION:Speakers: Ildar Musin (Institute of Mathematics with Computing Centre of RAS)\nFollowing the scheme of constructing of Gelfand-Shilov sp aces of type $S$ three new spaces of rapidly decreasing infinitely differe ntiable functions in ${\\mathbb R}^n$ will be defined with a help of famil ies of separately radial convex weight functions in ${\\mathbb R}^n$. Unde r some mild restrictions on weight functions these spaces will be characte rized via Fourier transforms. Some interesting particular cases of such sp aces corresponding to special families of weight functions will be conside red. This is a joint work with R.S. Yulmukhametov and A.V. Lutsenko.\n\nht tps://indico.eimi.ru/event/1238/contributions/539/ LOCATION: URL:https://indico.eimi.ru/event/1238/contributions/539/ END:VEVENT BEGIN:VEVENT SUMMARY:Isomorphic inverse problems DTSTART;VALUE=DATE-TIME:20230705T081000Z DTEND;VALUE=DATE-TIME:20230705T085500Z DTSTAMP;VALUE=DATE-TIME:20260807T110330Z UID:indico-contribution-1238-538@indico.eimi.ru DESCRIPTION:Speakers: Evgeny Korotyaev (Northeast Normal University)\nCons ider two inverse problems for Sturm-Liouville problems on the unit interv al. It means that there are two corresponding mappings $F\, f$ from a Hilb ert space of potentials $H$ into their spectral data. They are called is omorphic if $F$ is a composition of $f$ and some isomorphism $U$ of $H$ o nto itself. A isomorphic class is a collection of inverse problems isomorp hic to each other. We consider basic Sturm-Liouville problems on the unit interval and on the circle and describe their isomorphic classes of inver se problems. For example\, we prove that the inverse problems for the cas e of Dirichlet and Neumann boundary conditions are isomorphic. The proof i s based on the non-linear analysis.\n\nhttps://indico.eimi.ru/event/1238/c ontributions/538/ LOCATION: URL:https://indico.eimi.ru/event/1238/contributions/538/ END:VEVENT BEGIN:VEVENT SUMMARY:Rational trading in an efficient market and inequalities in analys is DTSTART;VALUE=DATE-TIME:20230705T133500Z DTEND;VALUE=DATE-TIME:20230705T140500Z DTSTAMP;VALUE=DATE-TIME:20260807T110330Z UID:indico-contribution-1238-524@indico.eimi.ru DESCRIPTION:Speakers: Nikolay Osipov (PDMI RAS)\nTrading in an efficient m arket where the asset price behaves as a martingale leads to a zero expect ed payoff. However\, the problem of how to make such trading as rational a s possible remains meaningful and non-trivial: it turns out that there is a certain gap between trading that has zero profit expectation\, but is st ill rational in the basic sense\, and completely irrational economic behav ior that violates the basic von Neumann--Morgenshtern rationality axioms. By solving the problem of describing this gap and finding optimal trading strategies that get into it\, we will arrive at the Bellman functions that have previously arisen in solving completely abstract problems about find ing sharp constants in inequalities from analysis. Namely\, solving the ec onomic problem in the absolute context\, where the strategy to be chosen d oes not depend on the current wealth of the agent\, we will arrive at the Bellman function related to the John--Nirenberg inequality in integral for m. Solving the problem in a relative context\, where all the agent's actio ns in the market are considered relative to his current wealth\, we will a rrive at the Bellman function related to the inequalities that describe th e relationship between Gehring classes. Thus\, we will obtain a natural ec onomic interpretation for the listed inequalities and the Bellman function s associated with them.\n\nhttps://indico.eimi.ru/event/1238/contributions /524/ LOCATION: URL:https://indico.eimi.ru/event/1238/contributions/524/ END:VEVENT BEGIN:VEVENT SUMMARY:Regular growth of Dirichlet series. Applications DTSTART;VALUE=DATE-TIME:20230705T070000Z DTEND;VALUE=DATE-TIME:20230705T074500Z DTSTAMP;VALUE=DATE-TIME:20260807T110330Z UID:indico-contribution-1238-525@indico.eimi.ru DESCRIPTION:Speakers: Ahtjar Gaisin (Institute of Mathematics with Computi ng Centre\, Ufa)\nThe report will focus on theorems of the minimum module type and their applications in the theory of the distribution of values.\ n\n For entire transcendental functions of finite order having the form $f (z)=\\sum\\limits_{n}a_{n}z^{p_{n}}$\, $p_{n}\\in\\mathbb{N}$\, G. Polia s howed that if the density of the sequence $\\left\\{p_{n}\\right\\}$ is e qual to zero\, then for any curve $\\gamma$ going to infinity\, there is a n unlimited sequence $\\{\\xi_{n}\\}\\subset\\gamma$\, such that for $\\xi _{n}\\rightarrow\\infty$ there is a relation:\n$$\\ln M_{f}(|\\xi_{n}|)\\s im \\ln\\left|f(\\xi_{n})\\right|$$\n($M_{f}(r)$ --- the maximum of the mo dule of the function $f$ on a circle of radius $r$). Later\, these results were completely transferred by I.D. Latypov to entire Dirichlet series of finite order and finite lower order by Ritt. A further generalization w as obtained in the works of N.N. Yusupova--Aitkuzhina to the more general classes $D(\\Phi)$ and $\\underline{D}(\\Phi)$ defined by the convex major ant $\\Phi$. In 2022 we obtained necessary and sufficient conditions for t he exponents $\\lambda_{n}$ under which the logarithm of the modulus of t he sum of any Dirichlet series from this classes on the curve $\\gamma$ o f a bounded $K$--slope was equivalent to the logarithm of the maximum term for $\\sigma=Re s\\rightarrow +\\infty$ over some asymptotic set whose up per density is not less than $\\frac{1}{\\sqrt{K^{2}+1}}$. It will be show n that this result can be amplified.\n\nThe results about iterations of en tire transcendental functions with a regular behavior of the modulus minim um will be presented in the report.\n\nhttps://indico.eimi.ru/event/1238/c ontributions/525/ LOCATION: URL:https://indico.eimi.ru/event/1238/contributions/525/ END:VEVENT BEGIN:VEVENT SUMMARY:On informationally complete operator-valued measures on locally co mpact groups DTSTART;VALUE=DATE-TIME:20230704T081000Z DTEND;VALUE=DATE-TIME:20230704T085500Z DTSTAMP;VALUE=DATE-TIME:20260807T110330Z UID:indico-contribution-1238-498@indico.eimi.ru DESCRIPTION:Speakers: Grigori Amosov ()\nLet $\\mathfrak G$ and $\\mathfra k {B}(\\mathfrak {G})$ be a locally compact Abelian group with a Haar meas ure $\\mu $ and the algebra of all measurable sets on $\\mathfrak G$ corre spondingly. Denote $B(H)_+$ the cone of positive linear operators acting i n a separable Hilbert space $H$. A map $\\mathfrak {M}:\\mathfrak {B}(\\ma thfrak {G})\\to B(H)_+$ is said to be a positive operator-valued measure ( POVM) on $\\mathfrak G$ if\n$$\n\\mathfrak{M} (\\cup_j B_j)=\\sum \\limits _j\\mathfrak{M}(B_j)\, \\quad B_j\\cap B_k=\\emptyset\, \\quad B_j\\in \\ mathfrak{B}(\\mathfrak {G})\, j\\neq k\,\n$$\n$$\n\\mathfrak {M}(\\emptyse t )=0\, \\quad \\mathfrak {M}(\\mathfrak {G})={\\rm I}.\n$$\nLet $\\mathfr ak {G}=\\hat G\\times G$ be the locally compact Abelian group generated by a locally compact Abelian group $(G\,\\nu)$ and\n$\\mu =\\hat \\nu \\time s \\nu $ be the Haar measure on $\\mathfrak {G}$. Then\, a projective unit ary representation $(\\chi \,g)\\to U_{\\chi \,g}$ of $\\mathfrak {G}$ in $H=L^2(G\,\\nu )$ defined by the formulla\n$$\n[U_{\\chi \,g}\\psi ](h)=[ \\chi (g)]^{1/2}\\chi (h)\\psi (h+g)\, \\quad g\,h\\in G\, \\quad \\chi \\ in \\hat G\, \\quad \\psi \\in H\,\n$$\nis irreducible and $\\mathfrak M ( B)=\\int \\limits_B U_{\\chi\,g} P_{0} U_{\\chi\, g}^*d\\mu(\\chi\,g)$\, w here $P_0$ is an arbitrary one-dimensional projection on the subspace $\\{ \\mathbb{C}\\xi_0\\}$\, is a POVM on $\\mathfrak{G}$ being covariant in t he sense [1-2]\n$$\nU_{\\chi\,g}\\mathfrak{M}(B)U_{\\chi\,g}^*=\\mathfrak{ M}(B+(\\chi\,g))\, \\quad (\\chi\,g)\\in \\mathfrak{G}\, \\quad B\\in \\ma thfrak{B}(\\mathfrak {G}).\n$$\nGiven a state (a positive unit-trace oper ator) $\\rho $ the function $F_{\\rho}$ on $\\mathfrak {G}$ determined as \n$$\nF_{\\rho }(\\chi \,g)=(U_{\\chi \,g}\\xi _0\,\\rho U_{\\chi \,g}\\xi _0)\n\\qquad \\qquad \\qquad (1)\n$$ \nis a density of probability distr ibution {$\\{ {\\rm Tr}(\\rho \\mathfrak {M}(B))\,\\\, B\\in \\mathfrak {M (G)} \\}$}. The POVM $\\mathfrak {M}=$ {$\\{ \\mathfrak {M}(B)\,\\ B\\in \ \mathfrak {M(G)} \\}$} is said to be informationally complete if (1) can b e can be converted. We show that (1) is informationally complete [3]. To prove this fact we investigate the set of contractions $T_{\\chi \,g}$ gen erated by the POVM $\\mathfrak {M}$.\n\nReferences:\n\n\n[1] G.G. Amosov\, On quantum tomography on locally compact groups\, Physics Letters A\, 43 1 (2022)\, 128002\, 7 pp.\n\n[2] G.G. Amosov\, On quantum channels generat ed by covariant positive operator-valued measures on a locally compact gro up\, Quantum Information processing\, 21 (2022)\, 81\, 15 pp.\n\n[3] G.G. Amosov\, On constructing informationally complete covariant positive opera tor-valued measures\, arXiv:2301.12492\n\nhttps://indico.eimi.ru/event/123 8/contributions/498/ LOCATION: URL:https://indico.eimi.ru/event/1238/contributions/498/ END:VEVENT BEGIN:VEVENT SUMMARY:B. Ya. Levin function for some sets of segments DTSTART;VALUE=DATE-TIME:20230701T122000Z DTEND;VALUE=DATE-TIME:20230701T125000Z DTSTAMP;VALUE=DATE-TIME:20260807T110330Z UID:indico-contribution-1238-537@indico.eimi.ru DESCRIPTION:Speakers: Nikolai Shirokov (St.-Petersburg State University an d National Research University High School of Economics in SPb)\nLet $\\{I _k\\}_{k\\in \\mathbb{Z}}$ be a set of disjoint of segments of real axis\, $E=\\bigcup_{k\\in \\mathbb{Z}}{I_k}$. We call the B.Ya.Levin function $f _{E\,\\sigma}(z)$\, $\\sigma >0$\, a function satisfying the following con ditions:\n\n1. $f_{E\,\\sigma}(z)$ is subharmonic on the complex plane $\\ mathbb{C}$ and harmonic on $\\mathbb{C}\\setminus E$\;\n\n2. $f_{E\,\\sigm a}(z)=0$\, $x\\in E$\; $f_{E\,\\sigma}(z)>0$\, $z\\in\\mathbb{C} \\setminu s E$\;\n\n3. $\\limsup_{z\\rightarrow \\infty}\\frac{f_{E\,\\sigma}(z)}{|z |}=\\sigma$\, $f_{E\,\\sigma}(\\bar{z})=f_{E\,\\sigma}(z)$\;\n\n4. If $g$ is subharmonic on $\\mathbb{C}$\, $g(x)\\leq 0$\, $x\\in E$\, $\\limsup_{z \\rightarrow \\infty}\\frac{g(z)}{|z|}\\leq\\sigma$\, then $g(z)\\leq f_{E \,\\sigma}(z)$.\n\nWe construct the B.Ya.Levin function for some sets of s egments such that $|I_k|_{|k|\\rightarrow \\infty}\\rightarrow 0$.\n\nhttp s://indico.eimi.ru/event/1238/contributions/537/ LOCATION: URL:https://indico.eimi.ru/event/1238/contributions/537/ END:VEVENT BEGIN:VEVENT SUMMARY:The Nuttall decomposition of a three-sheeted torus and the asympto tics of the rational Hermite-Pade approximants DTSTART;VALUE=DATE-TIME:20230701T081000Z DTEND;VALUE=DATE-TIME:20230701T085500Z DTSTAMP;VALUE=DATE-TIME:20260807T110330Z UID:indico-contribution-1238-533@indico.eimi.ru DESCRIPTION:Speakers: Semen Nasyrov (Kazan Federal University)\nWe study t he three-sheeted Riemann surface $S$ of genus $1$\,corresponding to the al gebraic function $w=\\sqrt[3]{(z-a_1)(z-a_2)(z-a_3)}$ with pairwise distin ct complex numbers $a_j$. There exists an abelian integral $G$ on $S$ whic h is regular on $S$\, except for three points lying over infinity where th e function Re $G$ has prescribed singularities of logarithmic type. \n\nT he harmonic function Re $G$ induces a partition of $S$ into three sheets\ ; it is called the Nuttall decomposition. Such decomposition plays an impo rtant role in investigation of the asymptotics of the rational Hermite-Pad e approximants. According to the Nuttall conjecture\, the sheet gluing lin es and their projections onto the Riemann sphere define the convergence do mains for the Hermite-Pade approximants. \n\nThe differential-topological structure of the Nuttall decomposition depends essentially on the mutual l ocation of the points $a_j$. A.I.Aptekarev and and D.N.Tulyakov (2016) des cribed the structure for the case when the triangle with vertices at the p oints $a_j$ is sufficiently close to the regular one. We consider the gene ral case and completely solve the problem for isosceles triangles with th e apex angle less than $\\pi/3$. In the talk we also discuss other cases. \n\nThe study was carried out at the expense of the grant of the Russian Science Foundation No.23-11-00066.\n\nhttps://indico.eimi.ru/event/1238/co ntributions/533/ LOCATION: URL:https://indico.eimi.ru/event/1238/contributions/533/ END:VEVENT BEGIN:VEVENT SUMMARY:Hardy spaces of fractional order DTSTART;VALUE=DATE-TIME:20230701T070000Z DTEND;VALUE=DATE-TIME:20230701T074500Z DTSTAMP;VALUE=DATE-TIME:20260807T110330Z UID:indico-contribution-1238-535@indico.eimi.ru DESCRIPTION:Speakers: Dmitrii Stolyarov (St. Petersburg State University)\ nThe space of measures of bounded total variation and $L_1$ quite often la ck good properties. Usually this is related to the unboundedness of the ma ximal function on $L_1$. The interest in these spaces is justified not onl y by the simplicity of their norms\, but also by direct connections with t he geometric measure theory\, and\, thus\, geometry. In harmonic analysis\ ,\nwe sometimes replace $L_1$ with a narrower space $H_1$. Here $H_1$ is t he real Hardy class\, it behaves ‘better’. However\, we lose the relat ionship with the geometric measure theory when passing to $H_1$: by ’the Riesz brothers’ theorem’ there are no analogs of the space of measure s whose norm resembles that of $H_1$. We will try to suggest a scale of sp aces that interpolates $L_1$ and $H_1$. These intermediate spaces do conta in singular measures of fractional dimension and also posses some properti es of the Hardy class\; for example\, some ’trace’ inequalities for fr actional integration operators are valid for measures in these spaces. We do not have complete proofs yet and are also slightly unsure whether our d efinitions are best possible. A larger part of work is done in a martingal e model that simplifies the classical setting of Euclidean spaces. Neverth eless\, the story seems worth telling. For example\, the aforementioned sc ale extends the definition of lower Hausdorff dimension to arbitrary distr ibutions.\n\nWork in progress with Daniel Spector\, Taiwan\n\nhttps://indi co.eimi.ru/event/1238/contributions/535/ LOCATION: URL:https://indico.eimi.ru/event/1238/contributions/535/ END:VEVENT BEGIN:VEVENT SUMMARY:Bounded BMO-regularity DTSTART;VALUE=DATE-TIME:20230705T141000Z DTEND;VALUE=DATE-TIME:20230705T144000Z DTSTAMP;VALUE=DATE-TIME:20260807T110330Z UID:indico-contribution-1238-534@indico.eimi.ru DESCRIPTION:Speakers: Dmitry Rutsky (St. Petersburg Department of Steklov Mathematical Institute of Russian Academy of Sciences)\nIn 1995\, N. Kalto n discovered that the stability of complex interpolation\n$(X_A\, Y_A)_\\t heta = \\left[ (X\, Y)_\\theta \\right]_A$ of a couple of Hardy-type space s for Banach lattices of measurable functions on the unit circle is charac terized in terms of the BMO-regularity property of lattice $X’ Y$\, that is\, the existence of majorants $w$ for arbitrary functions of the lattic e satisfying $\\log w \\in \\mathrm {BMO}$ with suitable estimates of the norms. BMO-regularity was studied extensively\, its most elegant equivale nt definition for couples of lattices is the existence of majorants $(u\, v)$ for arbitrary functions in $(X\, Y)$ satisfying $\\log u/v \\in \\math rm {BMO}$ with suitable control on the norms.\n\nA few years ago\, the sta bility of the real interpolation and the K-closedness of Hardy-type spaces were similarly characterized in terms of a weaker BMO-regularity property \, namely that a real interpolation space $(\\mathrm L_1\, X’ Y)_{\\thet a\, p}$ is BMO-regular. We will explore several alternative characterizat ions of this property that elucidate its relation to the usual BMO-regular ity.\n\nhttps://indico.eimi.ru/event/1238/contributions/534/ LOCATION: URL:https://indico.eimi.ru/event/1238/contributions/534/ END:VEVENT BEGIN:VEVENT SUMMARY:Representing systems of reproducing kernels in spaces of analytic functions DTSTART;VALUE=DATE-TIME:20230705T120500Z DTEND;VALUE=DATE-TIME:20230705T123500Z DTSTAMP;VALUE=DATE-TIME:20260807T110330Z UID:indico-contribution-1238-532@indico.eimi.ru DESCRIPTION:Speakers: Timur Batenev (Saint Petersburg University)\nIn the talk we give an elementary construction of reproducing kernels for Hardy s paces $H^p$\, $p\\in [1\,\\infty)$\, in polydisc\, ball and in half-plane\ , as well as representing systems of reproducing kernels in some weighted Hardy spaces in disc (e.g.\, Dirichlet space).\n\nhttps://indico.eimi.ru/e vent/1238/contributions/532/ LOCATION: URL:https://indico.eimi.ru/event/1238/contributions/532/ END:VEVENT BEGIN:VEVENT SUMMARY:Rotations of convex harmonic univalent mappings DTSTART;VALUE=DATE-TIME:20230706T090000Z DTEND;VALUE=DATE-TIME:20230706T094500Z DTSTAMP;VALUE=DATE-TIME:20260807T110330Z UID:indico-contribution-1238-531@indico.eimi.ru DESCRIPTION:Speakers: Ilgiz Kayumov (Kazan Federal University)\nI am going to describe recent results\, obtained jointly with S.Ponnusamy and Le Anh Xuan\, about some properties of convex harmonic mappings in the unit disk .\n\nhttps://indico.eimi.ru/event/1238/contributions/531/ LOCATION: URL:https://indico.eimi.ru/event/1238/contributions/531/ END:VEVENT BEGIN:VEVENT SUMMARY:Lp-Hardy-type inequalities for special weight functions DTSTART;VALUE=DATE-TIME:20230702T122000Z DTEND;VALUE=DATE-TIME:20230702T125000Z DTSTAMP;VALUE=DATE-TIME:20260807T110330Z UID:indico-contribution-1238-530@indico.eimi.ru DESCRIPTION:Speakers: Ramil Nasibullin (Kazan Federal University)\nWe prov e one-dimensional $𝐿_𝑝$-Hardy inequalities with additional terms and use them for justifying spatial analogues in convex domains with finite v olumes. We consider spatial inequalities in arbitrary domains\, and then we simplify them for convex domains. The constants in the additional terms in these spatial inequalities depend on the volume or on the diameter of the domain.\n\nhttps://indico.eimi.ru/event/1238/contributions/530/ LOCATION: URL:https://indico.eimi.ru/event/1238/contributions/530/ END:VEVENT BEGIN:VEVENT SUMMARY:Exponential series with a given growth majorant near the boundary DTSTART;VALUE=DATE-TIME:20230702T131500Z DTEND;VALUE=DATE-TIME:20230702T134500Z DTSTAMP;VALUE=DATE-TIME:20260807T110330Z UID:indico-contribution-1238-529@indico.eimi.ru DESCRIPTION:Speakers: Galiya Gaisina (Ufa University of Science and Techno logy)\nWe will talk about the behavior of series of exponents near the bou ndary in cases where the domain of regularity of the sum of the series is the entire plane\, a half-plane\, a bounded convex domain. Next\, we will touch the representation of analytic in the right half-plane functions by series of exponents\, taking into account a given convex majorant of growt h.\n\nhttps://indico.eimi.ru/event/1238/contributions/529/ LOCATION: URL:https://indico.eimi.ru/event/1238/contributions/529/ END:VEVENT BEGIN:VEVENT SUMMARY:Completeness of exponential systems in terms of mixed areas DTSTART;VALUE=DATE-TIME:20230704T090000Z DTEND;VALUE=DATE-TIME:20230704T094500Z DTSTAMP;VALUE=DATE-TIME:20260807T110330Z UID:indico-contribution-1238-528@indico.eimi.ru DESCRIPTION:Speakers: Bulat Khabibullin (Institute of Mathematics with CC of the Ufa FRC of RAS)\nWe give a scale of completeness conditions for exp onential systems in spaces of continuous functions on a compact set of the complex plane that are simultaneously holomorphic inside a compact set\, in spaces of holomorphic functions in a domain\, and so on. These conditio ns will be formulated in geometric terms of mixed areas for the convex hul l of a compact or domain. We will characterize the distribution of exponen ts of the exponential system both in terms of their modules and in terms o f arguments using various options for the convexity of functions. The vast majority of known results on the completeness of exponential systems in s uch spaces turn out to be very special cases from this scale. Our complete ness results extend to parameterized systems of entire functions\, which a re more general than exponential systems. All studies cover several comple x variables.\n\nhttps://indico.eimi.ru/event/1238/contributions/528/ LOCATION: URL:https://indico.eimi.ru/event/1238/contributions/528/ END:VEVENT BEGIN:VEVENT SUMMARY:Extensions of conditionally completely positive maps between opera tor systems DTSTART;VALUE=DATE-TIME:20230705T124000Z DTEND;VALUE=DATE-TIME:20230705T131000Z DTSTAMP;VALUE=DATE-TIME:20260807T110330Z UID:indico-contribution-1238-527@indico.eimi.ru DESCRIPTION:Speakers: Vsevolod Yashin (MIPT\, Steklov Mathematical Institu te of RAS\, Russian Quantum Center)\nIn noncommutative probability theory\ , conditionally completely positive maps arise as the generators of unital completely positive semigroups. We will propose a generalized definition for conditionally completely positive maps between (possibly different) op erator systems and in the finite dimensional case we will prove Arveson-ty pe theorem on the extension of conditionally completely positive maps.\n\n https://indico.eimi.ru/event/1238/contributions/527/ LOCATION: URL:https://indico.eimi.ru/event/1238/contributions/527/ END:VEVENT BEGIN:VEVENT SUMMARY:Refinement of powered Bohr inequality DTSTART;VALUE=DATE-TIME:20230701T131500Z DTEND;VALUE=DATE-TIME:20230701T134500Z DTSTAMP;VALUE=DATE-TIME:20260807T110330Z UID:indico-contribution-1238-526@indico.eimi.ru DESCRIPTION:Speakers: Diana Khammatova (Kazan Federal University)\nLet B d enote the class of all analytic functions mapping the unit disk into itsel f. We consider the powered Bohr sum of a function from the class B with an additional term including the area of the image of the disk of radius r. In this setting\, we prove a counterpart of the Bohr theorem for two diffe rent cases.\n\nhttps://indico.eimi.ru/event/1238/contributions/526/ LOCATION: URL:https://indico.eimi.ru/event/1238/contributions/526/ END:VEVENT BEGIN:VEVENT SUMMARY:Blashke $C^*$-algebras DTSTART;VALUE=DATE-TIME:20230702T135000Z DTEND;VALUE=DATE-TIME:20230702T142000Z DTSTAMP;VALUE=DATE-TIME:20260807T110330Z UID:indico-contribution-1238-522@indico.eimi.ru DESCRIPTION:Speakers: Alla Kuznetsova (Kazan Federal University)\nThe idea of the talk is to bring together the well known Blaschke product and oper ator algebras. We suggest the notion of the Blaschke $C^*$-algebra\, which is the universal $C^*$-algebra generated by some relations. The relations are defined by a family of finite Blaschke products. In this way we exte nd the Coburn’s Theorem for a family of non-unitary isometries connected by a family of finite Blaschke products. We show that the Blaschke $C^*$- algebras is isomorphic to the inductive limit of Toeplitz algebras.\nThe t alk is based on the joint work with Tamara Grigoryan.\n\nhttps://indico.ei mi.ru/event/1238/contributions/522/ LOCATION: URL:https://indico.eimi.ru/event/1238/contributions/522/ END:VEVENT BEGIN:VEVENT SUMMARY:Dominant sets for model spaces in several variables DTSTART;VALUE=DATE-TIME:20230706T095000Z DTEND;VALUE=DATE-TIME:20230706T103500Z DTSTAMP;VALUE=DATE-TIME:20260807T110330Z UID:indico-contribution-1238-521@indico.eimi.ru DESCRIPTION:Speakers: Evgueni Doubtsov (St. Petersburg Department of V.A. Steklov Mathematical Institute)\nLet $H^2 = H^2(B_n)$ denote the standard Hardy space on the open unit ball $B_n$ of $\\mathbb{C}^n$\, $n\\ge 2$\, a nd let $\\sigma$ denote the normalized Lebesgue measure on the unit sphere $\\partial B_n$. Given an inner function $I$\, a Lebesgue measurable set $E\\subset \\partial B_n$ is said to be dominant for the large model space $H^2 \\ominus I H^2$ if $\\sigma(E) < 1$ and $\\|f\\|_{H^2}^2 \\le C\\int _E |f|^2\\\, d\\sigma$ for all $f\\in H^2 \\ominus I H^2$. We use Clark me asures to construct dominant sets for an arbitrary inner function. This re search was supported by Russian Science Foundation (grant No. 19-11-00058) .\n\nhttps://indico.eimi.ru/event/1238/contributions/521/ LOCATION: URL:https://indico.eimi.ru/event/1238/contributions/521/ END:VEVENT BEGIN:VEVENT SUMMARY:The Bohr radius of a pair of operators DTSTART;VALUE=DATE-TIME:20230701T135000Z DTEND;VALUE=DATE-TIME:20230701T142000Z DTSTAMP;VALUE=DATE-TIME:20260807T110330Z UID:indico-contribution-1238-520@indico.eimi.ru DESCRIPTION:Speakers: Ramis Khasyanov (SPbU)\nIn 1914\, H. Bohr\, studying Dirichlet series\, discovered the following interesting fact in complex a nalysis\, which is now called the Bohr phenomenon:\n\n\nTheorem.\nLet $f(z )=\\sum_{n\\ge 0}a_nz^n$ and $\\|f\\|_{\\infty}:=\\sup_{z\\in \\mathbb{D}} |f(z) |$ in the unit disc $\\mathbb{D}=\\{|z|<1\\}$. Then\n$M_rf:=\\sum_{n \\ge 0}^{} |a_n| r^n\\le \\|f\\|_{\\infty}\, \\:\\:\n0\\le r\\le 1/3.$\nMo reover\, the constant $1/3$ is the best possible.\n\n\nWe introduce the co ncept of the Bohr radius of a pair of operators\, in terms of which many w ell-known results related to the Bohr inequality can be formulated. The re port will discuss questions about the Bohr radius for the differential ope rators\, Hadamard convolution operators\, and other operators. Using the c oncept of the Bohr radius of a pair of operators\, we generalize the theor em of B.Bhowmik and N.Das on the comparison of majorant series of subordin ate functions.\n\nhttps://indico.eimi.ru/event/1238/contributions/520/ LOCATION: URL:https://indico.eimi.ru/event/1238/contributions/520/ END:VEVENT BEGIN:VEVENT SUMMARY:Nontriviality of Siddiqi class and nonspanning systems of exponent ials on curves DTSTART;VALUE=DATE-TIME:20230701T142500Z DTEND;VALUE=DATE-TIME:20230701T145500Z DTSTAMP;VALUE=DATE-TIME:20260807T110330Z UID:indico-contribution-1238-519@indico.eimi.ru DESCRIPTION:Speakers: Rashit Gaisin (Institute of Mathematics with Computi ng Centre - Subdivision of the Ufa Federal Research Centre of Russian Acad emy of Science)\nWe study problem of noncompleteness of the system of expo nentials $\\{e^{\\pm \\lambda_n z}\\}$ $(\\lambda_n>0)$ in the space of co ntinuous functions on the arc of bounded slope. In the terms of minorant s equence we have obtained new equivalent condition\, which is sufficient fo r noncompleteness of the given system of exponentials. We also have proved that Siddiqi class is nontrivial if sequence $\\{M_n^c\\}$ satisfyes the A-condition.\n\nhttps://indico.eimi.ru/event/1238/contributions/519/ LOCATION: URL:https://indico.eimi.ru/event/1238/contributions/519/ END:VEVENT BEGIN:VEVENT SUMMARY:On a sufficient condition for the existence of unconditional bases of reproducing kernels in Fock type spaces with nonradial weights DTSTART;VALUE=DATE-TIME:20230705T113000Z DTEND;VALUE=DATE-TIME:20230705T120000Z DTSTAMP;VALUE=DATE-TIME:20260807T110330Z UID:indico-contribution-1238-500@indico.eimi.ru DESCRIPTION:Speakers: Konstsntin Isaev ()\nWe consider Fock type spaces\, the spaces $\\mathcal F_{\\varphi}$ of entire functions $f$ such that $fe^ {-\\varphi}\\in L_2(\\mathbb C)$\, where $\\varphi$ is a subharmonic funct ion. We have obtained new sucient conditions for the existence of uncondit ional bases of reproducing kernels (or Riesz bases of normalized\nreproduc ing kernels) in Fock type spaces with nonradial weights. The issue on exis tence of unconditional bases of reproducing kernels is actively studied du e to the fact\, in particular\, that this question is closely related to s uch classical problems of complex analysis as the problem of representing of functions by exponential series and the problem of interpolation by ent ire functions.\n\nhttps://indico.eimi.ru/event/1238/contributions/500/ LOCATION: URL:https://indico.eimi.ru/event/1238/contributions/500/ END:VEVENT BEGIN:VEVENT SUMMARY:Some asymptotic formulas connected with Bessel analysis DTSTART;VALUE=DATE-TIME:20230702T090000Z DTEND;VALUE=DATE-TIME:20230702T094500Z DTSTAMP;VALUE=DATE-TIME:20260807T110330Z UID:indico-contribution-1238-499@indico.eimi.ru DESCRIPTION:Speakers: Sergey Platonov (Petrozavovsk State University)\nIn various sections of the classical Fourier Analysis\, the problem of the co nvergence of the integrals\n$$\n\\int\\limits_0^\\infty f(\\lambda t)\\\, g(t)\\\, dt \n$$\nas $\\lambda\\to+0$ and $\\lambda\\to +\\infty$ under va rious assumptions on the functions $f$ and $g$ are considered. \nIn the ta lk we study some analogues of such problems for weight integrals of the fo rm\n$$\n\\int\\limits_0^\\infty f(\\lambda t)\\\, g(t)\\\,t^{2\\alpha+1} \ \\, dt \, \\quad \\alpha>-1/2\,\n$$\nfor functions $f$ and $g$ from some w eighted functional classes that are connected with Fourier -- Bessel harmo nic analysis.\n\nhttps://indico.eimi.ru/event/1238/contributions/499/ LOCATION: URL:https://indico.eimi.ru/event/1238/contributions/499/ END:VEVENT END:VCALENDAR