Asymptotics of the Berezin transform and quantization on planar domains

DOI10.1215/S0012-7094-95-07902-2zbMath0848.30028OpenAlexW1567209865MaRDI QIDQ1900906

Miroslav Engliš

Publication date: 25 October 1995

Published in: Duke Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1215/s0012-7094-95-07902-2

zbMATH Keywords

Bergman spacequantizationreproducing kernelsBerezin transformautomorphic functions

Mathematics Subject Classification ID

Applications of functional analysis in quantum physics (46N50) Hilbert spaces with reproducing kernels (= (proper) functional Hilbert spaces, including de Branges-Rovnyak and other structured spaces) (46E22) Fuchsian groups and automorphic functions (aspects of compact Riemann surfaces and uniformization) (30F35) Kernel functions in one complex variable and applications (30C40)

Related Items (8)

The Berezin transform and its applications ⋮ QUANTIZATION METHODS: A GUIDE FOR PHYSICISTS AND ANALYSTS ⋮ Berezin-Toeplitz quantization for compact Kähler manifolds. A review of results ⋮ Trace formula of semicommutators ⋮ Helton-Howe trace, Connes-Chern characters and Toeplitz quantization of Bergman spaces ⋮ Berezin Quantization and Reproducing Kernels on Complex Domains ⋮ On a construction of L. Hua for positive reproducing kernels ⋮ A Forelli-Rudin construction and asymptotics of weighted Bergman kernels

Cites Work

• General concept of quantization
• An invariant volume-mean-value property
• Correspondence principle for the quantized annulus, Romanovski polynomials, and Morse potential
• Quantization of Kähler manifolds. III
• Functions invariant under the Berezin transform
• The Berezin transform and invariant differential operators
• Density of algebras generated by Toeplitz operators on Bergman spaces
• Non-perturbative deformation quantization of Cartan domains
• Quantization of Kähler manifolds. I: Geometric interpretation of Berezin's quantization
• Hankel Operators on Weighted Bergman Spaces
• QUANTIZATION
• Quantization of Kahler Manifolds. II
• Asymptotics of Reproducing Kernels on a Plane Domain
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