Journal of the
Korean Mathematical Society
JKMS

ISSN(Print) 0304-9914 ISSN(Online) 2234-3008

Article

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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.

A translation theorem for the generalized Fourier--Feynman transform associated with Gaussian process on function space

Seung Jun Chang, Jae Gil Choi, and Ae Young Ko

Dankook University, Dankook University, Dankook University

Abstract

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