Berezin transforms on pluriharmonic Bergman spaces

DOI10.1090/S0002-9947-08-04653-9zbMath1162.47028OpenAlexW2132428240MaRDI QIDQ3617610

Miroslav Engliš

Publication date: 30 March 2009

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

Full work available at URL: https://doi.org/10.1090/s0002-9947-08-04653-9

zbMATH Keywords

Berezin transformpluriharmonic Bergman kernel

Mathematics Subject Classification ID

Asymptotic approximations, asymptotic expansions (steepest descent, etc.) (41A60) Toeplitz operators, Hankel operators, Wiener-Hopf operators (47B35) Pluriharmonic and plurisubharmonic functions (31C10) 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 (6)

The Sarason sub-symbol and the recovery of the symbol of densely defined Toeplitz operators over the Hardy space ⋮ Berezin transform on the harmonic Fock space ⋮ On higher dimensional Luecking's theorem ⋮ Invariant symbolic calculus for compact Lie groups ⋮ Berezin transform and Toeplitz operators on harmonic Bergman spaces ⋮ Toeplitz operators on pluriharmonic function spaces: deformation quantization and spectral theory

Cites Work

• Domains with finite dimensional Bergman space
• Berezin and Berezin-Toeplitz quantizations for general function spaces
• Berezin transform on the harmonic Fock space
• Deformation estimates for the Berezin-Toeplitz quantization
• Toeplitz quantization of Kähler manifolds and \(gl(N)\), \(N\to \infty\) limits
• Weighted Bergman kernels and quantization
• Non-perturbative deformation quantization of Cartan domains
• QUANTIZATION IN COMPLEX SYMMETRIC SPACES
• Berezin Quantization and Reproducing Kernels on Complex Domains
• Estimates of the harmonic Bergman kernel on smooth domains
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