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Invertible measure preserving transformations and pointwise convergence


Author: J.-M. Belley
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
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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 $ \vert z\vert = 1$.


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

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1974-0335752-7
Article copyright: © Copyright 1974 American Mathematical Society

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