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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Invertible measure preserving transformations and pointwise convergence
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by J.-M. Belley PDF
Proc. Amer. Math. Soc. 43 (1974), 159-162 Request permission

Abstract:

An investigation of pointwise convergence of sequences $\{ \sum \nolimits _{j = - \infty }^\infty {a_j^kf({T^{ - j}}x):k = 1,2, \cdots } \}$ where $f$ lies in the space ${L^1}([0,1])$ of Lebesgue integrable functions on the unit interval, $T$ is an invertible measure preserving transformation on $[0,1]$, and the sequence of polynomials $\{ \sum \nolimits _{j = - \infty }^\infty {a_j^k{z^{ - j}}:k = 1,2, \cdots } \}$ is uniformly bounded and pointwise convergent for all $z$ such that $|z| = 1$.
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Additional Information
  • © Copyright 1974 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 43 (1974), 159-162
  • MSC: Primary 28A65
  • DOI: https://doi.org/10.1090/S0002-9939-1974-0335752-7
  • MathSciNet review: 0335752