A Fubini theorem for generalized analytic Feynman integrals and Fourier-Feynman transforms on function space
Bull. Korean Math. Soc. 2003 Vol. 40, No. 3, 437-456
Published online September 1, 2003
Seung Jun Chang and Il Yong Lee
Dankook University, Dankook University
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 $\sab$ 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, Fubini theorem
MSC numbers : 28C20, 60J65
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