Weighted Bergman spaces and the holomorphic discrete series of \(\widetilde{U(p,q)}\)

DOI10.1006/JFAN.1999.3553zbMath0957.43008OpenAlexW2000708938MaRDI QIDQ1568545

Salem Ben Said

Publication date: 27 August 2000

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

Full work available at URL: https://doi.org/10.1006/jfan.1999.3553

zbMATH Keywords

highest weight representationsweighted Bergman spacesreproducing kernelholomorphic discrete series

Mathematics Subject Classification ID

Harmonic analysis on homogeneous spaces (43A85) Semisimple Lie groups and their representations (22E46) Holomorphic functions of several complex variables (32A10)

Related Items (2)

Computation of weighted Bergman inner products on bounded symmetric domains and Parseval-Plancherel-type formulas under subgroups ⋮ Projections Separating Spectra for $\boldsymbol{L^2}$ on Pseudounitary Groups $\boldsymbol{{\mathrm U}(p,q)}$

Cites Work

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• Description of unitary representations with highest weight for groups U(p,q)
• Invariant cones in Lie algebras, Lie semigroups, and the holomorphic discrete series
• On the Segal-Shale-Weil representations and harmonic polynomials
• On Hardy and Bergman spaces on complex Ol'shanskiĭ semigroups
• Spherical functions on ordered symmetric spaces
• Function spaces on the Ol'shanskiĭ semigroup and the Gel'fand-Gindikin program
• Function spaces and reproducing kernels on bounded symmetric domains
• Composition Series for Analytic Continuations of Holomorphic Discrete Series Representations of SU(n, n)
• Hardy spaces and analytic continuation of Bergman spaces

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