[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.4134/BKMS.2003.40.3.437

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

Chang, Seung-Jun (DEPARTMENT OF MATHEMATICS, DANKOOK UNIVERSITY)
Lee, Il-Yong (DEPARTMENT OF MATHEMATICS, DANKOOK UNIVERSITY)

Publication Information

Bulletin of the Korean Mathematical Society / v.40, no.3, 2003 , pp. 437-456 More about this Journal

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;

Citations & Related Records

Times Cited By KSCI : 2 (Citation Analysis)

Reference
Cited By KSCI

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1	Seung Jun Chang. (2015) Integral Transforms and Special Functions A new aspect of the analytic Fourier-Feynman transform and its applications / 26 (1) , 65
1	Il Yong Lee. (2013) Bulletin of the Korean Mathematical Society A FUBINI THEOREM FOR GENERALIZED ANALYTIC FEYNMAN INTEGRAL ON FUNCTION SPACE / 50 (1) , 217
4	Seung Jun Chang. (2017) Mathematische Nachrichten Some relationships for the double modified generalized analytic function space Fourier-Feynman transform and its applications / 290 (4) , 520
9	(2018) Integral Transforms and Special Functions generalized analytic Fourier–Feynman transform / 29 (9) , 745