An Excursion into Berezin–Toeplitz Quantization and Related Topics

DOI10.1007/978-3-319-22407-7_2zbMath1341.53122OpenAlexW2405327937MaRDI QIDQ2798645

Miroslav Engliš

Publication date: 13 April 2016

Published in: Quantization, PDEs, and Geometry (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-3-319-22407-7_2

zbMATH Keywords

Toeplitz operatorBergman kernelBerezin transformBerezin quantizationBergmann space

Mathematics Subject Classification ID

Toeplitz operators, Hankel operators, Wiener-Hopf operators (47B35) Deformation quantization, star products (53D55) Hilbert spaces with reproducing kernels (= (proper) functional Hilbert spaces, including de Branges-Rovnyak and other structured spaces) (46E22) Bergman spaces of functions in several complex variables (32A36) Research exposition (monographs, survey articles) pertaining to differential geometry (53-02)

Related Items (16)

Berezin-Toeplitz quantization associated with higher Landau levels of the Bochner Laplacian ⋮ \(k\)-Hankel Wigner transform and its applications to the localization operators theory ⋮ Connection and curvature on bundles of Bergman and Hardy spaces ⋮ Helton-Howe trace, Connes-Chern characters and Toeplitz quantization of Bergman spaces ⋮ On an interpolation problem for the classical weighted harmonic Bergman space ⋮ Toeplitz Algebras on the Harmonic Fock Space ⋮ Semiclassical spectral analysis of Toeplitz operators on symplectic manifolds: the case of discrete wells ⋮ Bilinear localization operators on modulation spaces ⋮ \(k\)-Hankel Gabor transform on \(\mathbb{R}^d\) and its applications to the reproducing kernel theory ⋮ Time–frequency analysis associated with the generalized Wigner transform ⋮ A product expansion for Toeplitz operators on the Fock space ⋮ Co-Toeplitz operators and their associated quantization ⋮ 2-D covariant affine integral quantization(s) ⋮ Coherent states on the unit ball of C n and asymptotic expansion of their associated covariant symbol ⋮ Berezin-Toeplitz quantization on symplectic manifolds of bounded geometry ⋮ Berezin transform of two arguments

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