Remote Access Proceedings of the American Mathematical Society
Green Open Access

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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 60G15

Retrieve articles in all journals with MSC: 60G15

Additional Information

Keywords: Fernique, Gaussian, Banach, series, reproducing kernel
Article copyright: © Copyright 1972 American Mathematical Society