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Proceedings of the American Mathematical Society

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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
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 $|z| = 1$.

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Article copyright: © Copyright 1974 American Mathematical Society