Bulletin of the
Korean Mathematical Society BKMS

In this paper, we define an $L_p$ analytic generalized Fourier-Feynman transform and a convolution product of functionals in a Banach algebra $\mathcal F (C_{a,b}[0,T])$ which is called the Fresnel type class, and in more general class $\mathcal F_{A_1,A_2}$ of functionals defined on general function space $C_{a,b}[0,T]$ rather than on classical Wiener space. Also we obtain some relationships between the $L_p$ analytic generalized Fourier-Feynman transform and convolution product for functionals in $\mathcal F (C_{a,b}[0,T])$ and in $\mathcal F_{A_1,A_2}$.

Keywords: generalized Brownian motion process, generalized analytic Feynman integral, generalized analytic Fourier-Feynman transform, convolution product, Fresnel type class

MSC numbers: 60J25, 28C20