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Convergence for moving averages

Published online by Cambridge University Press:  19 September 2008

Alexandra Bellow ,
Roger Jones  and
Joseph Rosenblatt
Alexandra Bellow
Affiliation:
Mathematics Department, Northwestern University, Evanston, IL 60201, USA
Roger Jones
Affiliation:
Mathematics Department, DePaul University, 2323 N. Seminary, Chicago, IL 60614, USA
Joseph Rosenblatt
Affiliation:
Mathematics Department, Ohio State University, Columbus, OH 43210, USA
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Abstract

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Assume T is an ergodic measure preserving point transformation from a probability space onto itself. Let be a sequence of pairs of positive integers, and define the sequence of averaging operators . Necessary and sufficient conditions are given forthis sequence of averages to converge almost everywhere. Weighted versions are also considered.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 10 , Issue 1 , March 1990 , pp. 43 - 62
Copyright
Copyright © Cambridge University Press 1990

References

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