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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Functions in the Fresnel class


Authors: K. S. Chang, G. W. Johnson and D. L. Skoug
Journal: Proc. Amer. Math. Soc. 100 (1987), 309-318
MSC: Primary 42B10; Secondary 28C20, 60G15, 81C35
MathSciNet review: 884471
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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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DOI: http://dx.doi.org/10.1090/S0002-9939-1987-0884471-6
PII: S 0002-9939(1987)0884471-6
Article copyright: © Copyright 1987 American Mathematical Society