Functions in the Fresnel class

Chang, K. S.; Johnson, G. W.; Skoug, D. L.

doi:10.1090/S0002-9939-1987-0884471-6

Functions in the Fresnel class
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by K. S. Chang, G. W. Johnson and D. L. Skoug

Proc. Amer. Math. Soc. 100 (1987), 309-318

DOI: https://doi.org/10.1090/S0002-9939-1987-0884471-6

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Abstract:

Let $H$ be a separable infinite-dimensional Hilbert space over ${\mathbf {R}}$. The Fresnel class $\mathcal {F}(H)$ 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 $\mathcal {F}(H)$. 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.

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