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

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 $\small{S(L^2_{a,b}[0,T])}$ 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
1.
A FUBINI THEOREM FOR GENERALIZED ANALYTIC FEYNMAN INTEGRAL ON FUNCTION SPACE,;;;

대한수학회보, 2013. vol.50. 1, pp.217-231
1.
A new aspect of the analytic Fourier-Feynman transform and its applications, Integral Transforms and Special Functions, 2015, 26, 1, 65
2.
A FUBINI THEOREM FOR GENERALIZED ANALYTIC FEYNMAN INTEGRAL ON FUNCTION SPACE, Bulletin of the Korean Mathematical Society, 2013, 50, 1, 217
3.
Some relationships for the double modified generalized analytic function space Fourier-Feynman transform and its applications, Mathematische Nachrichten, 2017, 290, 4, 520
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