We consider the problem of analytic continuation of power series in the sectoral domain by means of interpolation of coefficients by holomorphic functions. We explore the relationship between the growth (indicator) of the interpolating function and the set, to which the series can be extended.
To estimate the growth of a holomorphic function of several complex variables, we use a...
The variational method is one of the main methods for finding a region of a functional and boundary mappings. The greatest difficulty of this method is the study of the functional differential equation for the boundary mapping. V.V. Chernikov proposed a way for finding a solution to such a functional differential equation using the area method. We use the idea of V.V. Chernikov to study some...
The conjecture states that among all $n$-dimensional domains with given inradius $\delta_0$ the maximum of the best Brezis--Marcus constants $\lambda(\Omega)$ is given by $\lambda(B_n)$, where $B_n$ is the $n$-dimensional ball
of radius $\delta_0$. In the talk the known results in Hardy type inequalities with additional terms are presented and we will give review of our own results in...
We consider a nonsurjective convolution operator in the Beurling space of ultradifferentiable functions of mean type generated by the weight function $\omega$. We establish necessary and (separately) sufficient conditions on the symbol under which the range of the operator contains the space defined by another weight function and of another type. These results are applied to convolution...
In this talk we give applications of the conformal geometry to the spectral estimates of the Dirichlet-Laplace operator in bounded simply connected domains with highly non-rectifiable boundaries.
Our method is based on the geometrical theory of composition operators on Sobolev spaces. These composition operators are generated by conformal mappings.
The talk is based on a joint work with Ivan...
For $r\in(0,1)$ let $f_r(z) = f(rz)$. A well-known Weissler inequality states that for the Hardy spaces $H^p$ and $H^q$, $p\leq q$,
$\|f_r\|_{H^q}\leq \|f\|_{H^p}\qquad \Longleftrightarrow \qquad r\leq \sqrt{\frac pq}.$
We consider Bergman spaces $A^p(w)$ with the weight $w(r)\geq0$, consisting of functions $f$ analytic in the unit
disk $\mathbb{D}$ and such that
$\|f\|_{A^p(w)}...
The Gaudin model is a quantum integrable system originally introduced to describe the interaction of multiple charged particles on a line. It consists of $n$ commuting Hamiltonian operators, dependent on $n$ pairwise distinct complex parameters and acting on the tensor product of $n$ irreducible representations of the Lie algebra $\mathfrak{sl}_2$. One of the main tasks of the Gaudin model is...
We consider strongly elliptic second-order systems with constant coefficients in domains on the plane reduced to the canonical form with only two real parameters $\tau$, $\sigma\in[0, 1)$ and written in complex form. When both parameters are equal to zero, we obtain the complex Laplace equation. When only $\sigma=0$, we have the skew-symmetric system which is a perturbation of the Laplace one...
Traditionally, weak asymptotics of Hermite--Padé polynomials for various systems of Markov functions (such as the Angelesco and Nikishin systems) is described in terms of the vector potential problem on the complex plane. This approach has a number of limitations in context of generalisation of Stahl’s theory on Hermite--Padé polynomials. Development of the alternative language was initiated...
