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Keywords:
abstract Wiener space; conditional Wiener integral; conditional Fourier-Feynman transform; Fubini theorem
Summary:
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.
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