Integral transform and convolution of analytic functionals on abstract Wiener space

DOI10.1080/01630560008816942zbMath0948.28008OpenAlexW2102433886MaRDI QIDQ4484799

Byoung Soo Kim, Kun Soo Chang, Il Yoo

Publication date: 4 June 2000

Published in: Numerical Functional Analysis and Optimization (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/01630560008816942

zbMATH Keywords

Fourier-Feynman transformabstract Wiener spaceanalytic functionalsFourier-Wiener transform

Mathematics Subject Classification ID

Convolution as an integral transform (44A35) Set functions and measures and integrals in infinite-dimensional spaces (Wiener measure, Gaussian measure, etc.) (28C20)

Related Items (24)

Relationships for modified generalized integral transforms, modified convolution products and first variations on function space ⋮ Generalized integral transforms with the translation operator on function space ⋮ Parts formulas involving the Fourier-Feynman transform associated with Gaussian paths on Wiener space ⋮ Some properties of the matrix Wiener transform with related topics on Hilbert space ⋮ Some applications of the spectral theory for the integral transform involving the spectral representation ⋮ Some basic relationships among transforms, convolution products, first variations and inverse transforms ⋮ Unnamed Item ⋮ New expressions of the modified generalized integral transform via the translation theorem with applications ⋮ Generalized convolution product for an integral transform on a Wiener space ⋮ Unnamed Item ⋮ A new expression for the transform with respect to the Gaussian process ⋮ Relationships Involving Transforms and Convolutions Via the Translation Theorem ⋮ Analytic Fourier-Feynman transform and convolution of functionals on abstract Wiener space. ⋮ A FUBINI THEOREM FOR INTEGRAL TRANSFORMS AND CONVOLUTION PRODUCTS ⋮ A survey of results involving transforms and convolutions in function space ⋮ Relationships involving generalized fourier–feynman transform, convolution and first variation ⋮ Generalized integral transforms and convolution products on function space ⋮ Unnamed Item ⋮ A recurrence formula with respect to the Cameron–Storvick type theorem of the 𝒯-transform ⋮ Integral transforms of functionals in \(L^{2}(C_{a,b}[0,T)\)] ⋮ Fundamental formulas for modified generalized integral transforms ⋮ Convolution products, integral transforms and inverse integral transforms of functionals inL₂(C₀[0,T)] ⋮ ON THE STABILITY OF THE GENERALIZED QUADRATIC AND ADDITIVE FUNCTIONAL EQUATION IN RANDOM NORMED SPACES VIA FIXED POINT METHOD ⋮ Double integral transforms and double convolution products of functionals on abstract Wiener space

Cites Work

• An \(L_2\) analytic Fourier-Feynman transform
• Convolution and the Fourier-Wiener transform on abstract Wiener space
• Convolution in Fourier-Wiener transform
• Some examples of Fourier-Wiener transforms of analytic functionals
• Fourier-Wiener transforms of analytic functionals
• Approximation Methods for Singular Integral Equations with Conjugation on Curves with Corners

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