Conditional Fourier-Feynman transform given infinite dimensional conditioning function on abstract Wiener space - Choi, Jae Gil; Shim, Sang Kil (Czechoslovak mathematical journal, 2023)
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.