Vector valued Riesz distributions on Euclidian Jordan algebras |
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Authors: | Joachim Hilgert Karl-Hermann Neeb |
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Institution: | 1. Mathematisches Institut, Technische Universit?t Clausthal, Erzstr.1, D-38678, Clausthal-Zellerfeld, Germany 2. Arbeitsgruppe Funktionalanalysis, Technische Universit?t Darmstadt, Schlo?gartenstra?e 7, D-64289, Darmstadt, Germany
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Abstract: | Let V be a Euclidean Jordan algebra, Гthe associated symmetric cone and G be the identity component of the linear automorphism group of Г.In this paper we associate to a certain class of spherical representations (ρ, ɛ) of G certain ɛ-valued Riesz distributions
generalizing the classical scalar valued Riesz distributions on V. Our construction is motivated by the analytic theory of
unitary highest weight representations where it permits to study certain holomorphic families of operator valued Riesz distributions
whose positive definiteness corresponds to the unitarity of a representation of the automorphism group of the associated tube
domain Г +iV. |
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Keywords: | Math Subject Classifications" target="_blank">Math Subject Classifications 22E46 17C50 |
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