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

Abstract

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.