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arXiv · 2306.14007

On the symbol calculus for multidimensional Hausdorff operators

E. Liflyand·A. Mirotin
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Abstract

The aim of this work is to derive a symbol calculus on $L^2(\mathbb{R}^n)$ for multidimensional Hausdorff operators. Two aspects of this activity result in two almost independent parts. While throughout the perturbation matrices are supposed to be self-adjoint and form a commuting family, in the second part they are additionally assumed to be positive definite. What relates these two parts is the powerful method of diagonalization of a normal Hausdorff operator elaborated earlier by the second author.

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E. Liflyand, A. Mirotin. 2023-06-24. On the symbol calculus for multidimensional Hausdorff operators. https://arxiv.org/abs/2306.14007

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