A Lipschitz estimate for Berezin’s operator calculus
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- by L. A. Coburn
- Proc. Amer. Math. Soc. 133 (2005), 127-131
- DOI: https://doi.org/10.1090/S0002-9939-04-07476-3
- Published electronically: August 20, 2004
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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, $\mathbf {C}^{n}$, 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.References
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Bibliographic Information
- L. A. Coburn
- Affiliation: Department of Mathematics, SUNY at Buffalo, Buffalo, New York 14260
- Email: lcoburn@acsu.buffalo.edu
- 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
- © Copyright 2004 American Mathematical Society
- 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
- MathSciNet review: 2085161