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)

 
 

 

On the convergence of multiplicatively orthogonal series


Author: C. J. Preston
Journal: Proc. Amer. Math. Soc. 28 (1971), 453-455
MSC: Primary 42.16
DOI: https://doi.org/10.1090/S0002-9939-1971-0284760-0
MathSciNet review: 0284760
Full-text PDF

Abstract | Similar Articles | Additional Information

Abstract: G. Alexits and A. Sharma have recently shown that if $ \{ {\varphi _n}\} _{n = 1}^\infty $ is a uniformly bounded multiplicatively orthogonal system on a finite measure space and if $ \{ {c_n}\} _{n = 1}^\infty $ is a sequence of real numbers with $ \sum _{n = 1}^\infty c_n^2 < \infty $, then the partial sums $ \sum _{k = 1}^n{c_{k\varphi k}}$ converge almost everywhere. We give here a simple proof of this result.


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 42.16

Retrieve articles in all journals with MSC: 42.16


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1971-0284760-0
Keywords: Uniformly bounded multiplicatively orthogonal systems, almost everywhere convergence
Article copyright: © Copyright 1971 American Mathematical Society

American Mathematical Society