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

Authors:	Seung Jun Chang Jae Gil Choi David Skoug

Affiliation:	Department of Mathematics, Dankook University, Cheonan 330-714, Korea ; Department of Mathematics, Dankook University, Cheonan 330-714, Korea ; Department of Mathematics and Statistics, University of Nebraska, Lincoln, Nebraska, 68588-0323

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 denotes the Paley-Wiener-Zygmund stochastic integral $int _{0}^{T} alpha (t) d x(t)$ .

Keywords:	Generalized Brownian motion process generalized analytic Feynman integral generalized analytic Fourier-Feynman transform first variation Cameron-Storvick type theorem

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