Representations in \(L^{2}\)-spaces on infinite-dimensional symmetric cones

DOI10.1006/jfan.2001.3884zbMath1004.22007OpenAlexW2083952723MaRDI QIDQ1604532

Karl-Hermann Neeb, Bent Orsted

Publication date: 4 July 2002

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

Full work available at URL: https://doi.org/10.1006/jfan.2001.3884

zbMATH Keywords

Laplace transformCayley transformWishart distributionsoperator-valued measuresunitary highest weight representationsinfinite-dimensional symmetric cones

Mathematics Subject Classification ID

Representations of Lie and linear algebraic groups over real fields: analytic methods (22E45)

Related Items (2)

Fock model and Segal-Bargmann transform for minimal representations of Hermitian Lie groups ⋮ Reflection positive stochastic processes indexed by Lie groups

Cites Work

• Analyticity in infinite dimensional spaces
• Operator-valued positive definite kernels on tubes
• Unitary highest weight representations in Hilbert spaces of holomorphic functions on infinite dimensional domains
• Holomorphy and convexity in Lie theory
• On nonlinear transformations of Gaussian measures
• The classification of locally finite split simple Lie algebras
• Distributions in Hilbert Space and Canonical Systems of Operators
• Holomorphic highest weight representations of infinite dimensional complex classical groups
• Algebraic integration theory
• Linear Symmetries of Free Boson Fields
• Vector valued Riesz distributions on Euclidean Jordan algebras
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