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.
Il Yong Lee, Jae Gil Choi, and Seung Jun Chang
Dankook University, Dankook University, Dankook University
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
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