Fourier-Feynman transforms and Wiener integrals over paths in abstract Wiener spaces

摘要

We establish some relationships between L_p-analytic Fourier-Feynman transforms and Wiener integrals over paths on C_0(B), the space of abstract Wiener space valued continuous functions on [0,T], for certain cylinder-type functions of the form F_(x) = f((h_1,x(s_1)),…,(h_1,x(s_n)),…,(h_m,x(s_1)),…,(h_m,x(s_n))), where f ∈ L_p (R~(mn)), 1 ≤ p ≤ 2 and 0 = s_0 ≤ s_1 ≤ … ≤ s_n = T is a partition of [0,T].