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

 

Note relating Bochner integrals and reproducing kernels to series expansions on a Gaussian Banach space


Author: Raoul D. LePage
Journal: Proc. Amer. Math. Soc. 32 (1972), 285-288
MSC: Primary 60G15
MathSciNet review: 0296987
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Abstract: Fernique's recent proof of finiteness of positive moments of the norm of a Banach-valued Gaussian random vector $ \mathfrak{X}$ is used to prove rth mean convergence of reproducing kernel series representations of $ \mathfrak{X}$. Embedding of the reproducing kernel Hilbert space into the Banach range of X is explicitly given by Bochner integration. This work extends and clarifies work of Kuelbs, Jain and Kallianpur.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1972-0296987-3
PII: S 0002-9939(1972)0296987-3
Keywords: Fernique, Gaussian, Banach, series, reproducing kernel
Article copyright: © Copyright 1972 American Mathematical Society