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Conditional Fourier-Feynman transform given infinite dimensional conditioning function on abstract Wiener space
Czechoslovak Mathematical Journal, Tome 73 (2023) no. 3, pp. 849-868
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We study a conditional Fourier-Feynman transform (CFFT) of functionals on an abstract Wiener space $(H,B,\nu )$. 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 $\mathcal F(B)$ and we finally investigate some Fubini theorems involving CFFT.
We study a conditional Fourier-Feynman transform (CFFT) of functionals on an abstract Wiener space $(H,B,\nu )$. 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 $\mathcal F(B)$ and we finally investigate some Fubini theorems involving CFFT.
DOI : 10.21136/CMJ.2023.0310-22
Classification : 28C20, 42B10, 46B09, 46G12
Keywords: abstract Wiener space; conditional Wiener integral; conditional Fourier-Feynman transform; Fubini theorem 
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Choi, Jae Gil; Shim, Sang Kil. Conditional Fourier-Feynman transform given infinite dimensional conditioning function on abstract Wiener space. Czechoslovak Mathematical Journal, Tome 73 (2023) no. 3, pp. 849-868. doi: 10.21136/CMJ.2023.0310-22

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