Abstract. We first study the generalized Fourier-Gauss transforms of functionals defined on the complexification B C of an abstract Wiener space (H, B, ν). Secondly, we introduce a new class of convolution products of functionals defined on B C and study several properties of the convolutions. Then we study various relations among the first variation, the convolutions, and the generalized Fourier-Gauss transforms.

Abstract. In this article, we consider a complex-valued and a measure-valued measure on C [0, t], the space of all real-valued continuous functions on [0, t]. Using these concepts, we establish the measure-valued Feynman-Kac formula and we prove that this formula satisfies a Volterra integral equation. The work here is patterned to some extent on earlier works by Kluvanek in 1983 and by Lapidus in 1987, but the present setting requires a number of new concepts and results.

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