Bochner and Schoenberg theorems on symmetric spaces in the complex case

DOI10.24033/bsmf.2247zbMath0829.43020OpenAlexW340948370MaRDI QIDQ4320460

Piotr Graczyk, Jean-Jacques Loeb

Publication date: 1 February 1995

Published in: Bulletin de la Société mathématique de France (Search for Journal in Brave)

Full work available at URL: http://www.numdam.org/item?id=BSMF_1994__122_4_571_0

zbMATH Keywords

Bochner theorempositive definite functionsspherical Fourier transformSchoenberg theoremLevy-Khinchine formulae

Mathematics Subject Classification ID

Harmonic analysis on homogeneous spaces (43A85) Differential geometry of symmetric spaces (53C35) Analysis on other specific Lie groups (43A80) Harmonic analysis and spherical functions (43A90)

Related Items (9)

Positive-definiteness and integral representations for special functions ⋮ A Laplace-type representation of the generalized spherical functions associated with the root systems of type \(A\) ⋮ WIENER TAUBERIAN THEOREMS FOR CERTAIN BANACH ALGEBRAS ON REAL RANK ONE SEMISIMPLE LIE GROUPS ⋮ The measure transition problem for meromorphic polar functions ⋮ An analogue of Bochner's theorem for Damek-Ricci spaces ⋮ Complex positive definite functions on strips ⋮ Positive definite holomorphic functions on tube domains. ⋮ Harmonic analysis on conelike bodies and holomorphic functions on tube domains ⋮ Characterizations of the beta distribution on symmetric matrices

Cites Work

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• A central limit theorem on the space of positive definite symmetric matrices
• Spherical functions on a real semisimple Lie group. A method of reduction to the complex case
• Cramér theorem on symmetric spaces of noncompact type
• The central limit theorem on spaces of positive definite matrices
• Infinitely divisible probabilities on the hyperbolic plane
• Isotropic infinitely divisible measures on symmetric spaces
• Dirichlet forms on symmetric spaces

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