Article
Kyungpook Mathematical Journal 2024; 64(2): 219-233
Published online June 30, 2024 https://doi.org/10.5666/KMJ.2024.64.2.219
Copyright © Kyungpook Mathematical Journal.
Generalized Fourier–Feynman Transform of Bounded Cylinder Functions on the Function Space Ca,b[0, T]
Jae Gil Choi
Department of Mathematics, Dankook University, Cheonan 31116, Republic of Korea
e-mail : jgchoi@dankook.ac.kr
Received: August 5, 2023; Revised: January 19, 2024; Accepted: March 10, 2024
In this paper, we study the generalized Fourier–Feynman transform (GFFT) for functions on the general Wiener space Ca,b[0, T]. We establish an explicit evaluation formula for the analytic GFFT of bounded cylinder functions on Ca,b[0, T]. We start by examining certain cylinder functions which belong in a Banach algebra of bounded functions on Ca,b[0, T]. We then obtain an explicit formula for the analytic GFFT of the bounded cylinder functions.
Keywords: generalized Brownian motion process, general Wiener space, generalized analytic Feynman integral, generalized analytic Fourier&ndash,Feynman transform, cylinder function