Communications of the
Korean Mathematical Society CKMS

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