Artem Dudko

collaborators

3 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.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 $Γ$ denote either its associated topological full group or the full group of a Bratteli diagram associated with $(X, T)$ . In this pap…

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 $ω\in\{0,…

Towards a Theory of Dobrakov-Sobolev Spaces

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