Laplace and Segal--Bargmann transforms on Hermitian symmetric spaces and orthogonal poly\-nomials.

DOI10.1016/S0022-1236(03)00101-0zbMath1035.32014arXivmath/0206275OpenAlexW2000874765MaRDI QIDQ1413971

Genkai Zhang, Mark G. Davidson, Gestur Olafsson

Publication date: 17 November 2003

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

Full work available at URL: https://arxiv.org/abs/math/0206275

zbMATH Keywords

Laplace transformpolynomialsOrthogonal polynomialsJordan pairsHighest weight representationsBounded symmetric domainsBranching ruleHolomorphic discrete seriesJack symmetricReal bounded symmetric domains

Mathematics Subject Classification ID

Harmonic analysis on homogeneous spaces (43A85) Connections of hypergeometric functions with groups and algebras, and related topics (33C80) Laplace transform (44A10) Hermitian symmetric spaces, bounded symmetric domains, Jordan algebras (complex-analytic aspects) (32M15)

Related Items (20)

Segal-Bargmann transforms associated with finite Coxeter groups ⋮ Laguerre functions on symmetric cones and recursion relations in the real case ⋮ QUANTIZATION METHODS: A GUIDE FOR PHYSICISTS AND ANALYSTS ⋮ Branching problems in reproducing kernel spaces ⋮ Stratonovich-Weyl correspondence for compact semisimple Lie groups ⋮ Isometry theorem for the Segal-Bargmann transform on a noncompact symmetric space of the complex type ⋮ Hardy spaces for non-compactly causal symmetric spaces and the most continuous spectrum ⋮ Hermitian symmetric spaces of tube type and multivariate Meixner-Pollaczek polynomials ⋮ Unnamed Item ⋮ Branching laws for minimal holomorphic representations ⋮ The Poisson transform on a compact real analytic Riemannian manifold ⋮ Generating functions associated to highest weight representations ⋮ Commuting Toeplitz operators on bounded symmetric domains and multiplicity-free restrictions of holomorphic discrete series ⋮ Differential recursion relations for Laguerre functions on symmetric cones. ⋮ Unnamed Item ⋮ TUBE DOMAINS AND RESTRICTIONS OF MINIMAL REPRESENTATIONS ⋮ The Segal-Bargmann transform for noncompact symmetric spaces of the complex type ⋮ Differential equations and recursion relations for Laguerre functions on symmetric cones ⋮ Branching coefficients of holomorphic representations and Segal-Bargmann transform ⋮ Coherent states and Berezin quantization for non-scalar holomorphic representations

Cites Work

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