Conditional Fourier-Feynman transform given infinite dimensional conditioning function on abstract Wiener space

We study a conditional Fourier-Feynman transform (CFFT) of functionals on an abstract Wiener space ( H , B , v ). An infinite dimensional conditioning function is used to define the CFFT. To do this, we first present a short survey of the conditional Wiener integral concerning the topic of this pape...

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Bibliographic Details
Published in:Czechoslovak mathematical journal Vol. 73; no. 3; pp. 849 - 868
Main Authors: Choi, Jae Gil, Shim, Sang Kil
Format: Journal Article
Language:English
Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.10.2023
Springer Nature B.V
Subjects:
Analysis
Conditioning
Convex and Discrete Geometry
Euclidean space
Fourier transforms
Hilbert space
Integral equations
Integrals
Mathematical Modeling and Industrial Mathematics
Mathematics
Mathematics and Statistics
Metric space
Ordinary Differential Equations
Partial differential equations
28C20
46G12
Fubini theorem
42B10
conditional Wiener integral
conditional Fourier-Feynman transform
abstract Wiener space
46B09
ISSN:0011-4642, 1572-9141
Online Access:Get full text
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Summary:We study a conditional Fourier-Feynman transform (CFFT) of functionals on an abstract Wiener space ( H , B , v ). An infinite dimensional conditioning function is used to define the CFFT. To do this, we first present a short survey of the conditional Wiener integral concerning the topic of this paper. We then establish evaluation formulas for the conditional Wiener integral on the abstract Wiener space B . Using the evaluation formula, we next provide explicit formulas for CFFTs of functionals in the Kallianpur and Bromley Fresnel class ℱ ( B ) and we finally investigate some Fubini theorems involving CFFT.
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ISSN:0011-4642
1572-9141
DOI:10.21136/CMJ.2023.0310-22