紧阿贝尔群上的μ-Hankel算子

Pub Date : 2023-04-19 DOI:10.1007/s10476-023-0217-3

A. Mirotin

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引用次数: 0

摘要

最近引入并研究了可分离希尔伯特空间上的（μ；Γ）-Hankel算子（A.Mirotin和E.Kuzmenkova，Hilbert空间上的μ-Hankel算符，Opuscula Math.，41（2021），881–899）。本文致力于将（μ；Γ）-Hankel算子推广到紧致连通阿贝尔群上（一般不可分）Hardy空间的情形。在这种情况下，在一些自然条件下充分描述了有界（μ；Γ）-Hankel算子。还考虑了积分算子的例子。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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μ-Hankel operators on compact Abelian groups

(μ; ν)-Hankel operators between separable Hilbert spaces were introduced and studied recently (A. Mirotin and E. Kuzmenkova, μ-Hankel operators on Hilbert spaces, Opuscula Math., 41 (2021), 881–899). This paper is devoted to generalization of (μ; ν)-Hankel operators to the case of (non-separable in general) 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 also considered.

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