Generalized Fourier-Feynman transforms and a first variation on function space

In this paper we use a generalized Brownian motion process to define a generalized Feynman integral and a generalized Fourier-Feynman transform. We establish a translation theorem and use it to express the generalized Feynman integral of the first variation of a functional F in terms of the generali...

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Bibliographic Details
Published in:Integral transforms and special functions 2003-10, Vol.14 (5), p.375-393
Main Authors: Chang, Seung Jun, Skoug, David
Format: Article
Language:English
Subjects:
Cameron-Storvick Type Theorem
First Variation
Generalized Analytic Feynman Integral
Generalized Analytic Fourier-Feynman Transform
Translation Theorem
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Summary:In this paper we use a generalized Brownian motion process to define a generalized Feynman integral and a generalized Fourier-Feynman transform. We establish a translation theorem and use it to express the generalized Feynman integral of the first variation of a functional F in terms of the generalized Feynman integral of F multiplied by a linear factor. We establish some integration by parts formulas for generalized Feynman integrals and transforms. We also find the generalized Fourier-Feynman transform of a functional F belonging to a Banach algebra (L 2 a, b [0, T]) after it has been multiplied by n linear factors; none of these linear factors belong to (L 2 a, b [0, T]). Finally we established some new generalized Feynman integration formulas.
ISSN:1065-2469
1476-8291
DOI:10.1080/1065246031000074425