Orthogonal expansions related to compact Gelfand pairs

DOI10.1016/j.exmath.2017.10.005zbMath1407.43002arXiv1612.03718OpenAlexW2564855685MaRDI QIDQ1756136

Emilio Porcu, Christian Berg, Ana Paula Peron

Publication date: 11 January 2019

Published in: Expositiones Mathematicae (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1612.03718

zbMATH Keywords

spherical functionsGelfand pairspositive definite functionsspherical harmonics for real and complex spheres

Mathematics Subject Classification ID

Harmonic analysis on homogeneous spaces (43A85) Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Spherical harmonics (33C55) Harmonic analysis and spherical functions (43A90) Positive definite functions on groups, semigroups, etc. (43A35)

Related Items (6)

Multivariate Gaussian Random Fields over Generalized Product Spaces involving the Hypertorus ⋮ Series expansions among weighted Lebesgue function spaces and applications to positive definite functions on compact two-point homogeneous spaces ⋮ Approximation tools and decay rates for eigenvalues of integral operators on a general setting ⋮ A unified view of space-time covariance functions through Gelfand pairs ⋮ Schoenberg's theorem for positive definite functions on products: a unifying framework ⋮ Characterization of strict positive definiteness on products of complex spheres

Cites Work

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• An extension of a theorem of Schoenberg to products of spheres
• From Schoenberg coefficients to Schoenberg functions
• Introduction to harmonic analysis and generalized Gelfand pairs
• Generalized Zernike or disc polynomials
• Spherical harmonics
• Dirichlet forms on symmetric spaces
• Positive definite functions on spheres
• Positive definite kernels on complex spheres

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