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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



The Wiener closure theorems for abstract Wiener spaces

Authors: J. Kuelbs and V. Mandrekar
Journal: Proc. Amer. Math. Soc. 32 (1972), 169-178
MSC: Primary 28A40; Secondary 46G99
MathSciNet review: 0293053
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Abstract: We introduce $ {\mathcal{L}_1}$ and $ {\mathcal{L}_2}$ translates for functions in $ {\mathcal{L}_1}(\mu )$ and $ {\mathcal{L}_2}(\mu )$ where $ \mu $ is a Gaussian measure on a Banach space. With these translates and the Fourier-Wiener transforms defined by Cameron and Martin we obtain Wiener's closure theorem in $ {\mathcal{L}_2}(\mu )$ and in $ {\mathcal{L}_1}(\mu )$. Using the $ {\mathcal{L}_1}(\mu )$ results we indicate the analogue of the Wiener-Pitt Tauberian theorems for this setup.

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Keywords: Abstract Wiener space, Fourier-Wiener transform, Wiener closure theorems, Tauberian theorems
Article copyright: © Copyright 1972 American Mathematical Society