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A. R. Mirotin

Publications and source records attributed to A. R. Mirotin.

At least 19 recordsLinked to original sources
arXiv2026

Hausdorff Operators on de Branges Spaces and Paley-Wiener spaces

For a class of de Branges spaces containing polynomials, sufficient and necessary conditions are given for the boundedness and compactness of the Hausdorff operators under consideration. For the Paly-Wiener spaces we reduce the study of our Hausdorff operators to classical integral ones. The operators that appeared are Carleman and therefore closeble in $L^2(\mathbb{R})$. We obtain also conditions for boundedness, compactness and nuclearity of our operators in the Paley-Wiener space as well as the conditions for their belonging to the Hilbert-Schmidt class.

math.FA↗
arXiv2025

On Laplace transform on semitattices

The aim of this work is to prove inverse formulas for Laplace transform on semilattices of open-and-compact sets in a both discrete and non-discrete cases. These are partial answers to a question posed by Yu.~I.~Lyubich.

math.FA↗
arXiv2025

On the regularity of generic Hausdorff-type transformations

The general notion of a Hausdorff-type operator with a kernel depending on an external variable is introduced and generalizations and analogs of classical results on the regularity of various summation methods are proved for the case of such operators.

math.FA↗
arXiv2025

Boundedness of Hausdorff-type operators with two-variable kernels on Lebesgue spaces

A general concept of a Hausdorff-type operator that absorbs all types of operators bearing the name `` Hausdorff operator'' and many others is considered. The characteristic features of this concept are the consideration of kernels depending on an external variable and the action between two arbitrary different sets. Generalizations and analogs of classical results on $L^p$ boundedness of various type of Hausdorff operators are proved for the case of such operators.

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arXiv2024

On a general concept of a Hausdorff-type operator

A unified approach to the concept of a Hausdorff operator is proposed in such a way that a number of classical and new operators feet into the given definition. Conditions are given for the boundedness of the operators under consideration in $L^p$ and in the atomic Hardy space $H^1$, and their regularity property is investigated. Examples are considered. The author hopes that this approach will allow one to unify the study of a lot of extensions and analogs of the classical Hausdorff operator.

math.FA↗
arXiv2024

On boundedness of Hausdorff-type operators on Sobolev spaces

A new notion of a Hausdorff-type operator on function spaces over domains in Euclidean spaces is introduced, and a sufficient condition for the boundedness of this operator on Sobolev spaces is proved. It is shown that this condition cannot be weakened in general.

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arXiv2023

Criteria for Analyticity of Multidimensionally Subordinate Semigroups

Let $ψ$ be a Bernstein function in one variable. A.~Carasso and T.~Kato obtained necessary and sufficient conditions for $ψ$ to have a property that $ψ(A)$ generates a quasibounded holomorphic semigroup for every generator $A$ of a bounded $C_0$-semigroup in a Banach space and deduced necessary conditions as well. We generalize their results to the multidimensional case and also give sufficient conditions for the property mentioned above.

math.FA↗
arXiv2023

On the spectra of multidimensional normal discrete Hausdorff operators

In the paper the general case of a normal discrete Hausdorff operators in $L^2(\mathbb{R}^d)$ is considered. The main result states that under some natural arithmetic condition the spectrum of such an operator is rotationally invariant. Several special cases and examples are considered.

math.FA↗
arXiv2022

$μ$-Hankel Operators on Compact Abelian Groups

$(μ;ν)$-Hankel operators between separable Hilbert spaces were introduced and studied recently (\textit{$μ$-Hankel operators on Hilbert spaces}, Opuscula Math., \textbf{41} (2021), 881--899). This paper, is devoted to generalization of $(μ;ν)$-Hankel operators to the (non-separable in general) case of Hardy spaces over compact and connected Abelian groups. In this setting bounded $(μ;ν)$-Hankel operators are fully described under some natural conditions. Examples of integral operators are considered.

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arXiv2022

Hausdorff Operators on Compact Abelian Groups

Necessary and sufficient conditions are given for boundedness of Hausdorff operators on generalized Hardy spaces $H^p_E(G)$, real Hardy space $H^1_{\mathbb{R}}(G)$, $BMO(G)$, and $BMOA(G)$ for compact Abelian group $G$. Surprisingly, these conditions turned out to be the same for all groups and spaces under consideration. Applications to Dirichlet series are given. The case of the space of continuous functions on $G$ and examples are also considered.

math.FA↗
arXiv2020

On Hausdorff operators on homogeneous spaces of locally compact groups

Hausdorff operators on the real line and multidimensional Euclidean spaces originated from some classical summation methods. Now it is an active research area. Hausdorff operators on general groups were defined and studied by the author since 2019. The purpose of this paper is to define and study Hausdorff operators on Lebesgue and real Hardy spaces over homogeneous spaces of locally compact groups. We introduce in particular an atomic Hardy space over homogeneous spaces of locally compact groups and obtain conditions for boundedness of Hausdorff operators on such spaces. Several corollaries are considered and unsolved problems are formulated.

math.FA↗
arXiv2020

On compact Hankel operators over compact Abelian groups

We consider compact and connected Abelian group $G$ with a linearly ordered dual. Based on the description of the structure of compact Hankel operators over $G$, generalizations of the classical Kronecker, Hartman, Peller and Adamyan-Arov-Krein theorems are obtained. A generalization of Burling's invariant subspace theorem is also established. Applications are given to Hankel operators over discrete groups

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