A Lipschitz estimate for Berezin's operator calculus

L. A. Coburn

doi:10.1090/S0002-9939-04-07476-3

A Lipschitz estimate for Berezin's operator calculus

L. A. Coburn

Mathematics

University at Buffalo

Research output: Contribution to journal › Article › peer-review

28 Scopus citations

Abstract

F. A. Berezin introduced a general "symbol calculus" for linear operators on reproducing kernel Hilbert spaces. For the particular Hilbert space of Gaussian square-integrable entire functions on complex n-space, C ⁿ, we obtain Lipschitz estimates for the Berezin symbols of arbitrary bounded operators. Additional properties of the Berezin symbol and extensions to more general reproducing kernel Hilbert spaces are discussed.

Original language	English
Pages (from-to)	127-131
Number of pages	5
Journal	Proceedings of the American Mathematical Society
Volume	133
Issue number	1
DOIs	https://doi.org/10.1090/S0002-9939-04-07476-3
State	Published - Jan 2005

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AB - F. A. Berezin introduced a general "symbol calculus" for linear operators on reproducing kernel Hilbert spaces. For the particular Hilbert space of Gaussian square-integrable entire functions on complex n-space, C n, we obtain Lipschitz estimates for the Berezin symbols of arbitrary bounded operators. Additional properties of the Berezin symbol and extensions to more general reproducing kernel Hilbert spaces are discussed.

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JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

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A Lipschitz estimate for Berezin's operator calculus

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