Berezin kernels of tube domains

DOI10.1006/jfan.2000.3706zbMath0970.43003OpenAlexW2072808220MaRDI QIDQ5933450

Gerrit Van Dijk, Michael Pevzner

Publication date: 15 October 2001

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jfan.2000.3706

zbMATH Keywords

irreducible decompositionBerezin kernelscausal symmetric spacesholomorphic discrete series representationsJordan algebrasrestriction of unitary representationssemisimple Lie group

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) Jordan structures associated with other structures (17C50)

Related Items (12)

Berezin kernels and analysis on Makarevich spaces ⋮ Computation of weighted Bergman inner products on bounded symmetric domains and Parseval-Plancherel-type formulas under subgroups ⋮ Toeplitz quantization and asymptotic expansions for real bounded symmetric domains ⋮ Laplace and Segal--Bargmann transforms on Hermitian symmetric spaces and orthogonal poly\-nomials. ⋮ Berezin transform on real bounded symmetric domains ⋮ Branching laws for minimal holomorphic representations ⋮ Branching laws for discrete Wallach points ⋮ Covariant quantization: spectral analysis versus deformation theory ⋮ Branching problems for semisimple Lie groups and reproducing kernels ⋮ TUBE DOMAINS AND RESTRICTIONS OF MINIMAL REPRESENTATIONS ⋮ Berezin kernels and maximal degenerate representations associated with Riemannian symmetric spaces of Hermitian type ⋮ Branching coefficients of holomorphic representations and Segal-Bargmann transform

Cites Work

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• Group representations on spaces of distributions
• Algebraic structures of Makarevič spaces. I
• Function spaces on the Ol'shanskiĭ semigroup and the Gel'fand-Gindikin program
• \(L^ q\)-estimates of spherical functions and an invariant mean-value property
• The Berezin transform and invariant differential operators
• Berezin transform on real bounded symmetric domains
• QUANTIZATION IN COMPLEX SYMMETRIC SPACES
• Causal compactification and Hardy spaces
• Tensor Products of Analytic Continuations of Holomorphic Discrete Series

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