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arXiv · 2506.15173

Analytic Schur multipliers

Aleksei Aleksandrov·Vladimir Peller
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Abstract

We study in this paper analytic Schur multipliers on ${\Bbb C}_+^2$ and ${\Bbb D}^2$, i.e. Schur multipliers on ${\Bbb R}^2$ and ${\Bbb T}^2$ that are boundary-value functions of functions analytic in ${\Bbb C}_+^2$ and ${\Bbb D}^2$. Such Schur multipliers are important when studying properties of functions of maximal dissipative operators and contractions under perturbation. We show that if the boundary-value function of a Schur multiplier has certain regularity properties, then it can be represented as an element of the Haagerup tensor product of spaces of analytic functions with similar regularity properties.

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BibTeXRIS

Aleksei Aleksandrov, Vladimir Peller. 2025-06-18. Analytic Schur multipliers. https://arxiv.org/abs/2506.15173

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