Symmetric pairs, Gelfand pairs and pairs such that generating functions of zonal spherical functions define unitary operators -- the case of the compact type

DOI10.1016/j.jfa.2006.02.008zbMath1104.43008OpenAlexW1995640518MaRDI QIDQ852585

Shigeru Watanabe

Publication date: 15 November 2006

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

Full work available at URL: https://doi.org/10.1016/j.jfa.2006.02.008

zbMATH Keywords

generating functionGelfand pairRiemannian symmetric pairzonal spherical function

Mathematics Subject Classification ID

Harmonic analysis on homogeneous spaces (43A85) Harmonic analysis and spherical functions (43A90)

Related Items (1)

Jacobi polynomials and associated reproducing kernel Hilbert spaces

Cites Work

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• Hilbert spaces of analytic functions and the Gegenbauer polynomials
• Generating functions and integral representations for the spherical functions on some classical Gelfand pairs
• Hilbert spaces of analytic functions associated with generating functions of spherical functions on \(U(n)/ U(n-1)\)
• On linear functional operations and the moment problem for a finite interval in one or several dimensions
• 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
• \(q\)-analogue of the Watanabe unitary transform associated to the \(q\)-continuous Gegenbauer polynomials

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