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 | References | Similar Articles | Additional Information

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 where denotes the Paley-Wiener-Zygmund stochastic integral .

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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