Artem Dudko

collaborators

4 papers

math.FA2026

Towards a Theory of Dobrakov-Sobolev Spaces

Artem Yurievich Dudko

The aim of this paper is to introduce a generalization of Sobolev spaces based on the Dobrakov integral. More precisely, we consider the setting of Banach-valued functions and Fomi…

math.RT2026

Classification of indecomposable states on the infinite symmetric inverse semigroup invariant under the infinite symmetric group. Semifinite case

Artem Dudko, Nikolay I. Nessonov

Let $N$ be a set of the natural numbers. Symmetric inverse semigroup $R_{\infty}$ is the semigroup of all infinite 0-1 matrices $[g_{ij}]$ with at most one 1 in each row and…

math.GR2026

Characters and $I I_{1}$ -Factor Representations of Full Groups of Cantor Minimal Systems

Artem Dudko, Constantine Medynets

Let $(X, T)$ be a Cantor minimal system, and let $I^$ denote either its associated topological full group or the full group of a Bratteli diagram associated with $(X, T)$ . In this pa…

math.DS2025

Irreducible Koopman representations for nonsingular actions on boundaries of rooted trees

Alexandre I. Danilenko, Artem Dudko

Let $G$ be a countable branch group of automorphisms of a spherically homogeneous rooted tree. Under some assumption on finitarity of $G$ , we construct, for each sequence $Ï\in\{0…

Towards a Theory of Dobrakov-Sobolev Spaces

Classification of indecomposable states on the infinite symmetric inverse semigroup invariant under the infinite symmetric group. Semifinite case

Characters and II1​-Factor Representations of Full Groups of Cantor Minimal Systems

Irreducible Koopman representations for nonsingular actions on boundaries of rooted trees

Characters and $I I_{1}$ -Factor Representations of Full Groups of Cantor Minimal Systems