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

 

Polynomial approximation for a class of physical random variables


Authors: A. De Santis, A. Gandolfi, A. Germani and P. Tardelli
Journal: Proc. Amer. Math. Soc. 120 (1994), 261-266
MSC: Primary 60B12; Secondary 28C20, 46G12, 47N30
MathSciNet review: 1164142
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Abstract: In white noise theory on Hilbert spaces, it is known that maps which are uniformly continuous around the origin in the S-topology constitute an important class of "physical" random variables. We prove that random variables having such a continuity property can be approximated in the gaussian measure by polynomial random variables. The proof relies on representing functions which are uniformly S-continuous around the origin as the composition of a continuous map with a Hilbert-Schmidt operator.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1994-1164142-5
PII: S 0002-9939(1994)1164142-5
Article copyright: © Copyright 1994 American Mathematical Society