THE RIESZ REPRESENTATION THEOREM ON INFINITE DIMENSIONAL SPACES AND ITS APPLICATIONS

DOI10.1142/S0219025702000705zbMath1072.46028OpenAlexW2135541124MaRDI QIDQ4818886

Chen-Yuh Shih, Yuh-Jia Lee

Publication date: 24 September 2004

Published in: Infinite Dimensional Analysis, Quantum Probability and Related Topics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s0219025702000705

zbMATH Keywords

Riesz representation theoremWeierstrass approximation theoremnuclear spaces

Mathematics Subject Classification ID

White noise theory (60H40) Convergence of probability measures (60B10) Measures and integration on abstract linear spaces (46G12) Duality theory for topological vector spaces (46A20) Set functions and measures and integrals in infinite-dimensional spaces (Wiener measure, Gaussian measure, etc.) (28C20) Measure (Gaussian, cylindrical, etc.) and integrals (Feynman, path, Fresnel, etc.) on manifolds (46T12)

Cites Work

• Analytic version of test functionals, Fourier transform, and a characterization of measures in white noise calculus
• Spaces of white noise distributions: Constructions, descriptions, applications. I
• A generalization of the Riesz representation theorem to infinite dimensions
• Generalized functions on infinite dimensional spaces and its applications to white noise calculus
• Abstract Wiener processes and their reproducing Kernel Hilbert spaces
• Bounded Measures on Topological Spaces

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