Bergman kernel asymptotics for generalized Fock spaces

DOI10.1007/BF02790262zbMath0989.47021OpenAlexW2034857851MaRDI QIDQ5941778

Finbarr Holland, Richard Rochberg

Publication date: 1 August 2002

Published in: Journal d'Analyse Mathématique (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02790262

zbMATH Keywords

momentskernel functionBergman kernel functionasymptotic relations

Mathematics Subject Classification ID

Linear operator methods in interpolation, moment and extension problems (47A57) Hilbert spaces with reproducing kernels (= (proper) functional Hilbert spaces, including de Branges-Rovnyak and other structured spaces) (46E22) Integral representations; canonical kernels (Szeg?, Bergman, etc.) (32A25) Kernel operators (47B34)

Related Items

Asymptotic behavior of eigenvalues of Toeplitz operators on the weighted analytic spaces ⋮ Weighted Paley-Wiener spaces ⋮ Hankel operators on Fock spaces and related Bergman kernel estimates ⋮ Asymptotic behavior of Bergman kernels with logarithmic weight ⋮ Dixmier classes on generalized Segal-Bargmann-Fock spaces ⋮ Riesz bases of reproducing kernels in Fock-type spaces ⋮ Finite rank Hankel operators over the complex Wiener space ⋮ A Forelli-Rudin construction and asymptotics of weighted Bergman kernels

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Hankel forms and the Fock space
• On the \(\bar {\partial{}}\) equation in weighted \(L^ 2\) norms in \(\mathbb{C} ^ 1\)
• Beurling-type density theorems for weighted \(L^p\) spaces of entire functions
• Pointwise estimates for the weighted Bergman projection kernel in \({\mathbb C}^n\), using a weighted \(L^2\) estimate for the \(\bar\partial\) equation
• An inequality for Fourier-Laplace transforms of entire functions, and the existence of exponential frames in Fock space
• Trace ideal criteria for Toeplitz and Hankel operators on the weighted Bergman spaces with exponential type weights
• \(\overline\partial\) and Schrödinger operators
• A Generalisation of Stirling's Formula.
• Asymptotic behaviour of reproducing kernels of weighted Bergman spaces
• Berezin Quantization and Reproducing Kernels on Complex Domains
• A Characterization of the Exponential Function