Work

Analytic Schur multipliers

Year: 2026

Type: article

Abstract: We study in this paper analytic Schur multipliers on C + 2 \mathbb {C}_{+}^{2} and D 2 \mathbb {D}^{2} , i.e. Schur multipliers on R 2 \mathbb {R}^{2} and T 2 \mathbb {T}^{2} that are boundary-value functions of functions analytic in C + 2 \mathbb {C}_{+}^{2} and D 2 \mathbb {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.

Source: Proceedings of the American Mathematical Society

DOI: 10.1090/proc/17531

Authors: A. Aleksandrov, V. Peller

Institutions: Russian Academy of Sciences, St Petersburg University, St. Petersburg Department of Steklov Institute of Mathematics, Steklov Mathematical Institute

Language: English

Topic: Holomorphic and Operator Theory

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: Russian Science Foundation

Award: G4208807289