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

 

Support properties of Gaussian processes over Schwartz space


Author: M. Ann Piech
Journal: Proc. Amer. Math. Soc. 53 (1975), 460-462
MSC: Primary 60G15; Secondary 28A40, 81.60
MathSciNet review: 0391242
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Abstract: We utilize the concept of an abstract Wiener space to prove a converse to a theorem of Minlos, thereby obtaining necessary and sufficient conditions for a Hilbert subspace of $ \mathcal{S}'({{\text{R}}^d})$ to support a given Gaussian process over $ \mathcal{S}({{\text{R}}^d})$.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1975-0391242-8
PII: S 0002-9939(1975)0391242-8
Keywords: Gaussian process, Schwartz space, free Boson field, abstract Wiener space
Article copyright: © Copyright 1975 American Mathematical Society