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 $\int _{0}^{T} \alpha (t) d x(t)$.References
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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
- 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
- © Copyright 2003 American Mathematical Society
- 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
- MathSciNet review: 1975406