On the spectra of multidimensional normal discrete Hausdorff operators

2023/07/06 by А. Р. Миротин, Mirotin, A. R. · 1 citation
Mathematics · #46E30 (Secondary) #47A10 #47B15 #47B38 (Primary) #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Spectral Theory in Mathematical Physics #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2307.03271

openalex publication_date 2023/07/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In the paper the general case of a normal discrete Hausdorff operators in L²(ℝ^d) is considered. The main result states that under some natural arithmetic condition the spectrum of such an operator is rotationally invariant. Several special cases and examples are considered.

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• Boundedness of Hausdorff-type operators with two-variable kernels on Lebesgue spaces

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