Generalized Fourier-Feynman transform and sequential transforms on function space (Q2914426)

In this paper, the authors investigate the existence of the generalized Fourier-Feynman transform for bounded cylidrical functionals of the form \(F\) given by NEWLINE\[NEWLINEF(x)=\hat{\nu}((e_1, x)^{\sim}, \ldots, (e_n, x)^{\sim}),NEWLINE\]NEWLINE where \((e,x)^{\sim}\) denotes the Paley-Wiener-Zygmund stochastic integral with \(x\) in a very general function space \(C_{a,b}[0,T]\) and \(\hat\nu\) is the Fourier transform of a complex measure \(\nu\) on \(\mathcal{B}(\mathbb R^n)\) with finite total variation. They then define two sequential transforms of such cylinder functional. Finally, they establish that the one is to identify the generalized Fourier-Feynman transform and the other transform acts like an inverse generalized Fourier-Feynman transform.