Skip to Main Content

Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2024 MCQ for Proceedings of the American Mathematical Society is 0.85.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Norm convergent expansions for Gaussian processes in Banach spaces.
HTML articles powered by AMS MathViewer

by Naresh C. Jain and G. Kallianpur
Proc. Amer. Math. Soc. 25 (1970), 890-895
DOI: https://doi.org/10.1090/S0002-9939-1970-0266304-1

Abstract:

Several authors have recently shown that Brownian motion with continuous paths on $[0,1]$ can be expanded into a uniformly convergent (a.s.) orthogonal series in terms of a given complete orthonormal system (CONS) in its reproducing kernel Hilbert space (RKHS). In an earlier paper we generalized this result to Gaussian processes with continuous paths. Here we obtain such expansions for a Gaussian random variable taking values in an arbitrary separable Banach space. A related problem is also considered in which starting from a separable Hilbert space $H$ with a measurable norm $|| \cdot |{|_1}$ defined on it, it is shown that the corresponding abstract Wiener process has a $||\cdot |{|_1}$-convergent orthogonal expansion in terms of a CONS chosen from $H$.
References
Similar Articles
  • Retrieve articles in Proceedings of the American Mathematical Society with MSC: 60.50
  • Retrieve articles in all journals with MSC: 60.50
Bibliographic Information
  • © Copyright 1970 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 25 (1970), 890-895
  • MSC: Primary 60.50
  • DOI: https://doi.org/10.1090/S0002-9939-1970-0266304-1
  • MathSciNet review: 0266304