Integral Representations of Positive Definite Matrix-Valued Distributions on Cylinders

DOI10.2307/2001075zbMath0705.47012OpenAlexW4247482233MaRDI QIDQ3485477

Jürgen Friedrich

Publication date: 1989

Full work available at URL: https://doi.org/10.2307/2001075

zbMATH Keywords

integral representationlocally compact groupBochner-type theoremG-continuous matrix-valued positive definite distributionstrongly continuous positive definite operator-valued functions

Mathematics Subject Classification ID

Functions whose values are linear operators (operator- and matrix-valued functions, etc., including analytic and meromorphic ones) (47A56) Dilations, extensions, compressions of linear operators (47A20) Positive definite functions in one variable harmonic analysis (42A82) Measures and integration on abstract linear spaces (46G12) Distributions, generalized functions, distribution spaces (46F99) Positive definite functions on groups, semigroups, etc. (43A35) Probability measures on groups or semigroups, Fourier transforms, factorization (60B15) Other representations of locally compact groups (22D12)

Related Items (4)

Local group representations ⋮ On the Relation Between Positive Definite Functions and Generalized Toeplitz Kernels ⋮ Extensions of operator valued positive definite functions and commutant lifting on ordered groups ⋮ Semigroups of measures in non-commutative harmonic analysis

Cites Work

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• Gaussian measures in Banach spaces
• Selfadjoint extension operators commuting with an algebra
• On extensions of positive definite operator-valued functions
• An extension theorem for positive-definite functions
• The extension problem for positive-definite functions
• Spectral resolution groups of unitary operators
• Integral Representation of Functions and Distributions Positive Definite Relative to the Orthogonal Group
• On Functions Positive Definite Relative to the Orthogonal Group and the Representation of Functions as Hankel-Stieltjes Transforms
• Weighted H<scp>ardy</scp> Spaces on S<scp>iegel</scp>'s Half Planes
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