GENERALIZED FOURIER-FEYNMAN TRANSFORMS, CONVOLUTION PRODUCTS, AND FIRST VARIATIONS ON FUNCTION SPACE

In this paper we examine the various relationships that exist among the first variation, the convolution product and the Fourier-Feynman transform for functionals of the form F(x) = f(❬α₁, x❭, ..., ❬αn, x❭, with x in a very general function space Ca, b[0, T].

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Bibliographic Details
Published in:The Rocky Mountain journal of mathematics 2010-01, Vol.40 (3), p.761-788
Main Authors: CHANG, SEUNG JUN, CHOI, JAE GIL, SKOUG, DAVID
Format: Article
Language:English
Subjects:
28C20
60J65
Brownian motion
Continuous functions
convolution product
first variation
Function spaces
generalized analytic Feynman integral
generalized analytic Fourier-Feynman transform
Generalized Brownian motion process
Integers
Mathematical expressions
Mathematical functions
Mathematical integrals
Mathematical theorems
Stochastic processes
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Summary:In this paper we examine the various relationships that exist among the first variation, the convolution product and the Fourier-Feynman transform for functionals of the form F(x) = f(❬α₁, x❭, ..., ❬αn, x❭, with x in a very general function space Ca, b[0, T].
ISSN:0035-7596
1945-3795
DOI:10.1216/RMJ-2010-40-3-761