When is a Riesz distribution a complex measure?

DOI10.24033/bsmf.2617zbMath1263.43003arXiv0906.3027OpenAlexW2952776204MaRDI QIDQ2880701

Alan D. Sokal

Publication date: 14 April 2012

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

Full work available at URL: https://arxiv.org/abs/0906.3027

zbMATH Keywords

Laplace transformunitary representationdeterminantRadon measuresymmetric coneRiesz distributionWallach setEuclidean Jordan algebralocally finitelocal Laplace transformGindikin's theoremharmonic analysis on symmetric conespositive definite orbit

Mathematics Subject Classification ID

Operations with distributions and generalized functions (46F10) Harmonic analysis on homogeneous spaces (43A85) Laplace transform (44A10) Hermitian symmetric spaces, bounded symmetric domains, Jordan algebras (complex-analytic aspects) (32M15) Integral operators (47G10) Noncommutative Jordan algebras (17A15)

Related Items (3)

Sonine Formulas and Intertwining Operators in Dunkl Theory ⋮ Complete monotonicity for inverse powers of some combinatorially defined polynomials ⋮ Riesz distributions and Laplace transform in the Dunkl setting of type A

Cites Work

• Algebraic/combinatorial proofs of Cayley-type identities for derivatives of determinants and Pfaffians
• Proof of a conjecture of M.L. Eaton on the characteristic function of the Wishart distribution
• The noncentral Wishart as an exponential family, and its moments
• Algèbre de Jordan et ensemble de Wallach. (Jordan algebra and Wallach set)
• Invariant generalized functions in homogeneous domains
• Analytic continuation of the holomorphic discrete series of a semi-simple Lie group
• Characterization of the Jørgensen set in generalized linear models
• Positive Riesz distributions on homogeneous cones
• Meromorphic property of the functions \(P^ \lambda\)
• Function spaces and reproducing kernels on bounded symmetric domains
• The Analytic Continuation of the Discrete Series. II
• A weak criterion for vector-valued holomorphy
• Resolution of Singularities and Division of Distributions
• Analytic functions in topological vector-spaces
• Vector valued Riesz distributions on Euclidean Jordan algebras
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