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arXiv · 1902.07671

On the description of multidimensional normal Hausdorff operators on Lebesgue spaces

A. R. Mirotin
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Abstract

The main goal of this work is to examine the structure of normal Hausdorff operators on $\mathbb{R}^n$. We show that normal Hausdorff operator in $L^2(\mathbb{R}^n)$ is unitary equivalent to the operator of multiplication by some matrix-function (its matrix symbol) in the space $L^2(\mathbb{R}^n; \mathbb{C}^{2^n}).$ Several corollaries that show that properties of a Hausdorff operator are closely related to the properties of its symbol are considered. In particular, the norm and the spectrum of such operators are described in terms of the symbol.

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BibTeXRIS

A. R. Mirotin. 2019-02-20. On the description of multidimensional normal Hausdorff operators on Lebesgue spaces. https://arxiv.org/abs/1902.07671

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