Integration by parts formulas involving generalized Fourier-Feynman transforms on function space

Chang, Seung; Choi, Jae; Skoug, David

doi:10.1090/S0002-9947-03-03256-2

Integration by parts formulas involving generalized Fourier-Feynman transforms on function space
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by Seung Jun Chang, Jae Gil Choi and David Skoug PDF

Trans. Amer. Math. Soc. 355 (2003), 2925-2948 Request permission

Abstract:

In an upcoming paper, Chang and Skoug used a generalized Brownian motion process to define a generalized analytic Feynman integral and a generalized analytic Fourier-Feynman transform. In this paper we establish several integration by parts formulas involving generalized Feynman integrals, generalized Fourier-Feynman transforms, and the first variation of functionals of the form $F(x)=f(\langle \alpha _{1} , x\rangle , \dots , \langle \alpha _{n} , x\rangle )$ where $\langle {\alpha ,x}\rangle$ denotes the Paley-Wiener-Zygmund stochastic integral $\int _{0}^{T} \alpha (t) d x(t)$.

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