A FUBINI THEOREM FOR GENERALIZED ANALYTIC FEYNMAN INTEGRALS AND FOURIER-FEYNMAN TRANSFORMS ON FUNCTION SPACE

Chang, Seung-Jun; Lee, Il-Yong

doi:10.4134/BKMS.2003.40.3.437

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A FUBINI THEOREM FOR GENERALIZED ANALYTIC FEYNMAN INTEGRALS AND FOURIER-FEYNMAN TRANSFORMS ON FUNCTION SPACE

Journal title : Bulletin of the Korean Mathematical Society
Volume 40, Issue 3, 2003, pp.437-456
Publisher : The Korean Mathematical Society
DOI : 10.4134/BKMS.2003.40.3.437

Title & Authors

A FUBINI THEOREM FOR GENERALIZED ANALYTIC FEYNMAN INTEGRALS AND FOURIER-FEYNMAN TRANSFORMS ON FUNCTION SPACE
Chang, Seung-Jun; Lee, Il-Yong;

Abstract

In this paper we use a generalized Brownian motion process to define a generalized analytic Feynman integral. We then establish a Fubini theorem for the function space integral and generalized analytic Feynman integral of a functional F belonging to Banach algebra ${$S(L^2_{a,b}[0,T])$}$ and we proceed to obtain several integration formulas. Finally, we use this Fubini theorem to obtain several Feynman integration formulas involving analytic generalized Fourier-Feynman transforms. These results subsume similar known results obtained by Huffman, Skoug and Storvick for the standard Wiener process.

Keywords

generalized Brownian motion process;generalized analytic Feynman integral;generalized analytic Fourier-Feynman transform;Fubinitheorem;

Language

English

Cited by

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