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)



Orthogonal expansions of vectors in a Hilbert space for non-Gaussian measures

Author: Yoshiaki Okazaki
Journal: Proc. Amer. Math. Soc. 86 (1982), 638-640
MSC: Primary 60B11
MathSciNet review: 674096
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Let $ \mathcal{H}$ be a separable Hilbert space and $ \mu $ a probability Radon measure on $ \mathcal{H}$ of second order. Then there exist $ ({a_n}) \in {l^2}$, an O.N.S. $ ({x_n}) \subset \mathcal{H}$ and an O.N.S. $ ({\xi _n}) \subset H$ such that the orthogonal series $ \sum\nolimits_{n = 1}^\infty {{a_n}{\xi _n}(x){x_n}} $ converges in $ \mathcal{H}$ $ \mu $-almost everywhere and it holds that $ x = \sum\nolimits_{n = 1}^\infty {{a_n}{\xi _n}(x){x_n}} $, $ \mu $-almost everywhere, where $ H$ is the generating Hubert space of $ \mu $. In the case where $ \mu $ is a Gaussian measure, a similar result was proved by Kuelbs [2] in general Banach spaces.

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

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 60B11

Retrieve articles in all journals with MSC: 60B11

Additional Information

Keywords: Orthogonal expansion, generating Hilbert space
Article copyright: © Copyright 1982 American Mathematical Society

American Mathematical Society