Some linear dynamics of convolution operators on Sobolev spaces

Tabatabaie, Seyyed Mohammad; Pourgholamhossein, Mahmoud; Fallah, Zahra

doi:10.22075/ijnaa.2026.40379.5633

Some linear dynamics of convolution operators on Sobolev spaces

Articles in Press

Document Type : Research Paper

Authors

Seyyed Mohammad Tabatabaie

Mahmoud Pourgholamhossein

Zahra Fallah

Department of Mathematics, University of Qom, Qom, Iran

10.22075/ijnaa.2026.40379.5633

Abstract

In this paper, we study the linear dynamical properties of a convolution operator on a Sobolev space $H_\gamma^s$ in the context of locally compact abelian groups and commutative hypergroups. In particular, we provide sufficient conditions for a function to be a recurrent point for a sequence $(\widetilde T_{\nu_{k}})_{k}$ of convolution operators on the Sobolev space $H_\gamma^s(K)$, where $K$ is a compact commutative Pontryagin hypergroup.

Keywords

Sobolev space

convolution algebras

locally compact groups

Pontryagin hypergroups

convolution operators

topologically recurrent operator

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