Communications of the
Korean Mathematical Society

ISSN(Print) 1225-1763 ISSN(Online) 2234-3024



Commun. Korean Math. Soc. 2023; 38(4): 1141-1151

Online first article October 17, 2023      Printed October 31, 2023

Copyright © The Korean Mathematical Society.

Generalized Fourier--Feynman transforms and convolutions for exponential type functions of generalized Brownian motion paths

Jae Gil Choi

Dankook University


Let $C_{a,b}[0,T]$ denote the space of continuous sample paths of a generalized Brownian motion process (GBMP). In this paper, we study the structures which exist between the analytic generalized Fourier--Feynman transform (GFFT) and the generalized convolution product (GCP) for functions on the function space $C_{a,b}[0,T]$. For our purpose, we use the exponential type functions on the general Wiener space $C_{a,b}[0,T]$. The class of all exponential type functions is a fundamental set in \linebreak $L_2(C_{a,b}[0,T])$.

Keywords: Generalized Brownian motion process, generalized Fourier--Feynman transform, generalized convolution product, exponential type function

MSC numbers: Primary 28C20, 42B10; Secondary 46B09, 60J65

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