Hilbert spaces of analytic functions associated with generating functions of spherical functions on \(U(n)/ U(n-1)\)

DOI10.3792/PJAA.70.323zbMath0840.43009OpenAlexW2063875084MaRDI QIDQ1805021

Shigeru Watanabe

Publication date: 4 May 1995

Published in: Proceedings of the Japan Academy. Series A (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3792/pjaa.70.323

zbMATH Keywords

generating functionshomogeneous spacesGegenbauer polynomialsHermite polynomialsSegal-Bargmann spaceBargmann transformzonal spherical functionssymmetrical polynomials

Mathematics Subject Classification ID

Harmonic analysis on homogeneous spaces (43A85) Hilbert spaces of continuous, differentiable or analytic functions (46E20) Other transforms and operators of Fourier type (43A32) Harmonic analysis and spherical functions (43A90)

Related Items (2)

Symmetric pairs, Gelfand pairs and pairs such that generating functions of zonal spherical functions define unitary operators -- the case of the compact type ⋮ Generating functions of the Jacobi polynomials and related Hilbert spaces of analytic functions

Cites Work

• Deux cours d'analyse harmonique. École d'Été d'Analyse Harmonique de Tunis, 1984
• Hilbert spaces of analytic functions and the Gegenbauer polynomials
• Generating functions and integral representations for the spherical functions on some classical Gelfand pairs
• Generating function for the spherical functions on a Gelfand pair of exceptional type
• On a Hilbert space of analytic functions and an associated integral transform part I
• Composition Series and Intertwining Operators for the Spherical Principal Series. I

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