On the spectra of multidimensional normal discrete Hausdorff operators

TL;DR

This paper investigates the spectral properties of multidimensional normal discrete Hausdorff operators in $L^2( eal^d)$, showing that their spectra are rotationally invariant under certain conditions, with various examples illustrating these results.

Contribution

It establishes the spectral invariance under rotation for a broad class of multidimensional normal discrete Hausdorff operators, extending previous understanding in this area.

Findings

Spectra are rotationally invariant under specific conditions

Several special cases and examples demonstrate the main results

Provides new insights into the spectral structure of these operators

Abstract

In the paper the general case of a normal discrete Hausdorff operators in $L^2(\mathbb{R}^d)$ 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.