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


Authors: Seung Jun Chang, Jae Gil Choi and David Skoug
Journal: Trans. Amer. Math. Soc. 355 (2003), 2925-2948
MSC (2000): Primary 60J65, 28C20
DOI: https://doi.org/10.1090/S0002-9947-03-03256-2
Published electronically: February 25, 2003
MathSciNet review: 1975406
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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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Additional Information

Seung Jun Chang
Affiliation: Department of Mathematics, Dankook University, Cheonan 330-714, Korea
Email: sejchang@dankook.ac.kr

Jae Gil Choi
Affiliation: Department of Mathematics, Dankook University, Cheonan 330-714, Korea
Email: jgchoi@dankook.ac.kr

David Skoug
Affiliation: Department of Mathematics and Statistics, University of Nebraska, Lincoln, Nebraska, 68588-0323
Email: dskoug@math.unl.edu

DOI: https://doi.org/10.1090/S0002-9947-03-03256-2
Keywords: Generalized Brownian motion process, generalized analytic Feynman integral, generalized analytic Fourier-Feynman transform, first variation, Cameron-Storvick type theorem
Received by editor(s): September 6, 2002
Received by editor(s) in revised form: November 15, 2002
Published electronically: February 25, 2003
Additional Notes: The present research was conducted by the research fund of Dankook University in 2000
Article copyright: © Copyright 2003 American Mathematical Society

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