$\mu$-Hankel Operators on Compact Abelian Groups

TL;DR

This paper extends the concept of $(ta; u)$-Hankel operators to Hardy spaces over compact Abelian groups, providing a full description of bounded operators and exploring examples of integral operators.

Contribution

It generalizes $(ta; u)$-Hankel operators to non-separable Hardy spaces on compact Abelian groups and characterizes bounded operators in this setting.

Findings

Bounded $(ta; u)$-Hankel operators are fully characterized.

Examples of integral operators fitting the generalized framework are provided.

Abstract

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