Analytic Feynman integrals, Fourier-Feynman transforms and change of scale formula for Wiener integrals over paths on abstract Wiener spaces

We establish the analytic Wiener and Feynman integral theory for 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)))(similar to),..., ( h(1), x( s(n)))(similar to),..., ( h(m), x( s(1)))(similar to),..., ( h(m), x( s(n)))(similar to)), ( 1) where f is an element of L-p(R-mn), 1 <= p <= infinity, and 0 = s(0) <= s1 <= center dot center dot center dot <= s(n) = T is a partition of [0, T]. In addition, we establish some relationships between analytic Feynman integrals, Fourier - Feynman transforms and Wiener integrals and we prove the change of scale formula for Wiener integrals over paths on C-0(B) in abstract Wiener spaces.