No abstract

Cameron and Storvick discovered change of scale formulas for Wiener integrals of bounded functions in a Banach algebra S on classical Wiener space. Yoo and Skoug extended these results to abstract Wiener space for a more generalized Fresnel class F A 1 ,A 2 than the Fresnel class F (B) which corresponds to the Banach algebra S on classical Wiener space. In this paper we present a change of scale formula for Wiener integrals of functions on abstract Wiener space which need not be bounded or continuous. 2000 AMS Mathematics Subject Classification. 28C20.

ABSTRACT. Let H be a separable infinite-dimensional Hubert space over R. The Fresnel class T(H) of H consists of all Fourier-Stieltjes transforms of bounded Borel measures on H. There are several results insuring that various functions of interest in connection with the Feynman integral and quantum mechanics are in 7{H). We give a theorem which has most of these results as corollaries as well as many further corollaries involving the reproducing kernel Hubert spaces of Gaussian stochastic processes.