Convolution and Fourier-Feynman transforms
For a class of functionals on the Wiener space of the form \[ F(x)= \exp\Biggl\{\int^T_0 f(t,x(t))dt\Biggr\}, \] a new definition of the convolution product is proposed. This convolution product is commutative. The \(L_p\) analytic Fourier-Feynman transform, introduced by \textit{G. W. Johnson} and \textit{D. L. Skoug} [Mich. Math. J. 26, 103-127 (1979; Zbl 0409.28007)], is applied. It is shown that the transform of the convolution product is a product of the transforms. In general the convolution product is not associative. The list of cases is given when the associativity does hold.
scientific article; zbMATH DE number 1143471