Convolution and Analytic Fourier-Feynman Transforms Over Paths in Abstract Wiener Space

In this paper, we define an L_p analytic Fourier-Feynman transform on C_{0}(B) , the space of abstract Wiener space valued continuous functions on [0, T] . We establish existence theorems and inverse transform theorems of this transform for some classes of cylinder type functions on C_{0}(B) having the form F(x)= f( (h_1, x(s_1))^{\sim}, \ldots, (h_m,x(s_n))^{\sim}) . Moreover we present various relationships involving convolution and the transforms.