TRANSLATION THEOREMS FOR THE ANALYTIC FOURIER-FEYNMAN TRANSFORM ASSOCIATED WITH GAUSSIAN PATHS ON WIENER SPACE

In this article, we establish translation theorems for the analytic Fourier-Feynman transform of functionals in non-stationary Gaussian processes on Wiener space. We then proceed to show that these general translation theorems can be applied to two well-known classes of functionals; namely, the Banach algebra S introduced by Cameron and Storvick, and the space B-A((p)) consisting of functionals of the form F(x) = f(<alpha(1), x >,..., <alpha(n), x >), where <alpha, x > denotes the Paley Wiener Zygmund stochastic integral integral(T)(0) alpha(t)dx (t).