Functions in the Fresnel class

Abstract

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