Berezin transform on real bounded symmetric domains

DOI10.1090/S0002-9947-01-02832-XzbMath0965.22015OpenAlexW1867191164MaRDI QIDQ2716160

Genkai Zhang

Publication date: 6 June 2001

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

Full work available at URL: https://doi.org/10.1090/s0002-9947-01-02832-x

zbMATH Keywords

weighted Bergman spacesirreducible decompositionBerezin transformBerezin kernelreal bounded symmetric domains

Mathematics Subject Classification ID

Harmonic analysis on homogeneous spaces (43A85) Semisimple Lie groups and their representations (22E46) Hermitian symmetric spaces, bounded symmetric domains, Jordan algebras (complex-analytic aspects) (32M15) Differential geometry of symmetric spaces (53C35)

Related Items

Restriction of square integrable representations: discrete spectrum, Restriction to symmetric subgroups of unitary representations of rank one semisimple Lie groups, Berezin kernels and analysis on Makarevich spaces, Branching of metaplectic representation of 𝑆𝑝(2,ℝ) under its principal 𝕊𝕃(2,ℝ)-subgroup, Toeplitz quantization and asymptotic expansions: Peter-Weyl decomposition, Computation of weighted Bergman inner products on bounded symmetric domains and Parseval-Plancherel-type formulas under subgroups, Hardy spaces for non-compactly causal symmetric spaces and the most continuous spectrum, Toeplitz quantization and asymptotic expansions for real bounded symmetric domains, Laplace and Segal--Bargmann transforms on Hermitian symmetric spaces and orthogonal poly\-nomials., Branching laws for minimal holomorphic representations, Berezin kernels of tube domains, Branching laws for discrete Wallach points, Degenerate principal series representations and their holomorphic extensions, Holomorphic retractions and boundary Berezin transforms, Asymptotic expansions for Toeplitz operators on symmetric spaces of general type, Covariant quantization: spectral analysis versus deformation theory, TUBE DOMAINS AND RESTRICTIONS OF MINIMAL REPRESENTATIONS, Branching coefficients of holomorphic representations and Segal-Bargmann transform

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• General concept of quantization
• Jordan algebras and Capelli identities
• Canonical representations related to hyperbolic spaces
• \(L^ q\)-estimates of spherical functions and an invariant mean-value property
• The Berezin transform and invariant differential operators
• Generalized Bessel functions on symmetric spaces
• $L^2$-versions of the Howe correspondence I.
• Berezin kernels of tube domains