Bulletin of the
Korean Mathematical Society BKMS

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