Analytic Fourier–Feynman Transforms and Convolution Products Associated with Bounded Linear Operators on Abstract Wiener Space

In this paper, an analytic Fourier–Feynman transform(FFT) and a convolution product(CP) associated with bounded linear operator(BLOP)s on abstract Wiener space(AWS) B are defined. The existences of the FFT and the CP of certain bounded functionals on B are also provided. Additionally, three kinds of relationships between the FFT and the CP are investigated. It turned out in this paper that the relations between them as well as the concepts of the transform and the convolution involve previous researches performed with Gaussian processes on classical Wiener space C0[0,T]. That is, the Gaussian processes used in previous researches are Banach space BLOPs on C0[0,T].