On the convergence of multiplicatively orthogonal series
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- by C. J. Preston PDF
- Proc. Amer. Math. Soc. 28 (1971), 453-455 Request permission
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.References
Additional Information
- © Copyright 1971 American Mathematical Society
- 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