Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

Article

HOME ALL ARTICLES View

Bull. Korean Math. Soc. 2013; 50(1): 217-231

Printed January 31, 2013

https://doi.org/10.4134/BKMS.2013.50.1.217

Copyright © The Korean Mathematical Society.

A Fubini theorem for generalized analytic Feynman integral on function space

Il Yong Lee, Jae Gil Choi, and Seung Jun Chang

Dankook University, Dankook University, Dankook University

Abstract

In this paper we establish a Fubini theorem for generalized analytic Feynman integral and $L_1$ generalized analytic Fourier-Feynman transform for the functional of the form $$ F(x)= f(\gal{\alpha_1,x},\ldots,\gal{\alpha_m,x}), $$ where $\{\alpha_1,\ldots,\alpha_m\}$ is an orthonormal set of functions from $\Lab2$. We then obtain several generalized analytic Feynman integration formulas involving generalized analytic Fourier-Feynman transforms.

Keywords: generalized Brownian motion process, generalized analytic Feynman integral, generalized analytic Fourier-Feynman transform, Fubini theorem

MSC numbers: Primary 60J65, 28C20