J. Korean Math. Soc. 2016; 53(5): 991-1017
Online first article August 11, 2016 Printed September 1, 2016
https://doi.org/10.4134/JKMS.j150317
Copyright © The Korean Mathematical Society.
Seung Jun Chang, Jae Gil Choi, and Ae Young Ko
Dankook University, Dankook University, Dankook University
In this paper we define a generalized analytic Fourier--Feyn\-man transform associated with Gaussian process on the function space $C_{a,b}[0,T]$. We establish the existence of the generalized analytic Fourier--Feynman transform for certain bounded functionals on $C_{a,b}[0,T]$. We then proceed to establish a translation theorem for the generalized transform associated with Gaussian process.
Keywords: generalized Brownian motion process, Gaussian process, generalized analytic Feynman integral, generalized analytic Fourier--Feynman transform, translation theorem
MSC numbers: 28C20, 60J65, 60G15
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