Note relating Bochner integrals and reproducing kernels to series expansions on a Gaussian Banach space
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- by Raoul D. LePage PDF
- Proc. Amer. Math. Soc. 32 (1972), 285-288 Request permission
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
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Additional Information
- © Copyright 1972 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 32 (1972), 285-288
- MSC: Primary 60G15
- DOI: https://doi.org/10.1090/S0002-9939-1972-0296987-3
- MathSciNet review: 0296987