Analytic Fourier-Feynman transforms and convolution

Abstract

In this paper we develop an L p {L_p} Fourier-Feynman theory for a class of functionals on Wiener space of the form F ( x ) = f ( ∫ 0 T α 1 d x , … , ∫ 0 T α n d x ) F(x) = f(\int _0^T {{\alpha _1}dx, \ldots ,\int _0^T {{\alpha _n}dx)} } . We then define a convolution product for functionals on Wiener space and show that the Fourier-Feynman transform of the convolution product is a product of Fourier-Feynman transforms.