Operator-valued positive definite kernels on tubes

DOI10.1007/BF01473583zbMath0956.22003OpenAlexW1976075836MaRDI QIDQ1265689

Karl-Hermann Neeb

Publication date: 4 March 2001

Published in: Monatshefte für Mathematik (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/178829

zbMATH Keywords

Fourier transformsintegral representationconvex conelocally compact abelian grouppositive definite functiontube domainsReinhardt domainsSiegel domainstubesoperator valued measureunitary highest weight modulescone of positive operatorsNussbaum's theoremoperator-valued Bochner theoremultraweakly continuous positive definite functions

Mathematics Subject Classification ID

Vector-valued set functions, measures and integrals (28B05) Unitary representations of locally compact groups (22D10)

Related Items (13)

Tangent fields, intrinsic stationarity, and self similarity ⋮ Cylindrical Wigner measures ⋮ Operator-valued positive definite kernels and differentiable universality ⋮ A note on Herglotz's theorem for time series on function spaces ⋮ A matrix-valued Schoenberg's problem and its applications ⋮ Ground state properties in the quasiclassical regime ⋮ Reflection positivity and conformal symmetry ⋮ Generating functions associated to highest weight representations ⋮ Spherical functions on mixed symmetric spaces ⋮ Vector valued Riesz distributions on Euclidean Jordan algebras ⋮ Standard subspaces of Hilbert spaces of holomorphic functions on tube domains ⋮ Reflection positive one-parameter groups and dilations ⋮ Representations in \(L^{2}\)-spaces on infinite-dimensional symmetric cones

Cites Work

• The Hausdorff-Bernstein-Widder theorem for semi-groups in locally compact Abelian groups
• A geometric approach to the Bohr compactification of cones
• Holomorphic representation theory. I
• Integral representation of dominated operations on spaces of continuous vector fields
• Über Bernoullische Zahlen in reell-quadratischen Zahlkörpern
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