Parts formulas involving the Fourier-Feynman transform associated with Gaussian paths on Wiener space

Park and Skoug established several integration by parts formulas involving analytic Feynman integrals, analytic Fourier-Feynman transforms, and the first variation of cylinder-type functionals of standard Brownian motion paths in Wiener space C-0[0, T]. In this paper, using a very general Cameron-Storvick theorem on the Wiener space C-0[0, T], we establish various integration by parts formulas involving generalized analytic Feynman integrals, generalized analytic Fourier-Feynman transforms, and the first variation (associated with Gaussian processes) of functionals F on C-0[0, T] having the form F(x) = f (alpha(1), x),..., (alpha(n), x)) for scale-invariant almost every x is an element of C-0[0, T], where (alpha, x) denotes the Paley-Wiener-Zygmund stochastic integral integral(T)(0) alpha(t)dx(t), and {alpha(1),...,alpha(n)} is an orthogonal set of nonzero functions in L-2[0, T]. The Gaussian processes used in this paper are not stationary.