Relationship Between the Analytic Generalized Fourier–Feynman Transform and the Function Space Integral

Abstract

In this paper we investigated a relationship between the analytic generalized Fourier–Feynman transform associated with Gaussian process and the function space integral for exponential type functionals on the function space $$C_{a,b}[0,T]$$ C a , b [ 0 , T ] . The function space $$C_{a,b}[0,T]$$ C a , b [ 0 , T ] can be induced by a generalized Brownian motion process. The Gaussian processes used in this paper are neither centered nor stationary.