GENERALIZED TRANSFORMS AND GENERALIZED CONVOLUTION PRODUCTS ASSOCIATED WITH GAUSSIAN PATHS ON FUNCTION SPACE

摘要

In this paper we define a more general convolution product (associated with Gaussian processes) of functionals on the function space C-a,C-b [0,T]. The function space C-a,C-b [0,T] is induced by a generalized Brownian motion process. Thus the Gaussian processes used in this paper are non-centered processes. We then develop the fundamental relationships between the generalized Fourier-Feynman transform associated with the Gaussian process and the convolution product.