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Roger L. Jones
Ergodic Theory and Connections with Analysis and Probability
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| Published: |
December 17, 1997 |
| Keywords: |
almost everywhere convergence, ergodic averages, strong sweeping out, convolution powers, oscillation inequalities, jump inequalities, variational inequalities, maximal functions, square functions, Calderón-Zygmund decomposition, Bourgain's entropy theorem |
| Subject: |
Primary: 28D05, 42B20; Secondary: 40A05, 42A50, 42B25, 60G42 |
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Abstract
In this paper we establish a variety or results in ergodic theory by
using techniques from probability and analysis. We discuss divergence
of operators, including strong sweeping out and Bourgain's entropy
method. We consider square functions, oscillation operators, and
variational operators for ergodic averages. We also consider almost
everywhere convergence of convolution powers.
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| Acknowledgements
R. Jones is partially supported by NSF Grant DMS-9531526
This paper is based on a series of three talks given at the New York Journal of Mathematics Conference, which was held at Albany, N.Y. from June 9 - June 14, 1997.
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| Author information
Department of Mathematics, DePaul University, 2219 N. Kenmore, Chicago IL 60614
rjones@condor.depaul.edu
http://www.depaul.edu/~rjones/
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