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A Lipschitz estimate for Berezin's operator calculus


Author: L. A. Coburn
Journal: Proc. Amer. Math. Soc. 133 (2005), 127-131
MSC (2000): Primary 47B32; Secondary 32A36
DOI: https://doi.org/10.1090/S0002-9939-04-07476-3
Published electronically: August 20, 2004
MathSciNet review: 2085161
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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, ${\text{\bf C}}^{n}$, 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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Additional Information

L. A. Coburn
Affiliation: Department of Mathematics, SUNY at Buffalo, Buffalo, New York 14260
Email: lcoburn@acsu.buffalo.edu

DOI: https://doi.org/10.1090/S0002-9939-04-07476-3
Received by editor(s): July 8, 2003
Received by editor(s) in revised form: August 15, 2003, and September 5, 2003
Published electronically: August 20, 2004
Communicated by: Joseph A. Ball
Article copyright: © Copyright 2004 American Mathematical Society

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