On the derivatives of the Berezin transform

DOI10.1090/S0002-9939-06-08238-4zbMath1094.47034OpenAlexW1561242235MaRDI QIDQ5290019

Genkai Zhang, Miroslav Engliš

Publication date: 24 April 2006

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0002-9939-06-08238-4

zbMATH Keywords

Bergman kernelFock spacebounded symmetric domainBerezin transforminvariant differential operatorSegal--Bargmann space

Mathematics Subject Classification ID

Hermitian symmetric spaces, bounded symmetric domains, Jordan algebras (complex-analytic aspects) (32M15) Bergman spaces of functions in several complex variables (32A36) Linear operators in reproducing-kernel Hilbert spaces (including de Branges, de Branges-Rovnyak, and other structured spaces) (47B32)

Related Items (8)

Berezin's operator calculus and higher order Schwarz–Pick lemma ⋮ The Berezin transform and its applications ⋮ The Berezin transform and Laplace-Beltrami operator ⋮ Derivatives of the Berezin transform ⋮ The Berezin transform and 𝑚th-order Bergman metric ⋮ Directional derivative estimates for Berezin's operator calculus ⋮ Covariant derivatives of the Berezin transform ⋮ Sharp Berezin Lipschitz estimates

Cites Work

• Approximation and symbolic calculus for Toeplitz algebras on the Bergman space
• A Lipschitz estimate for Berezin’s operator calculus
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