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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 815726, 5 pages
http://dx.doi.org/10.1155/2013/815726
Research Article

Linear Sequences and Weighted Ergodic Theorems

Korteweg-de Vries Institute for Mathematics, University of Amsterdam, P.O. Box 94248, 1090 GE Amsterdam, The Netherlands

Received 14 February 2013; Accepted 23 April 2013

Academic Editor: Baodong Zheng

Copyright © 2013 Tanja Eisner. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We present a simple way to produce good weights for several types of ergodic theorem including the Wiener-Wintner type multiple return time theorem and the multiple polynomial ergodic theorem. These weights are deterministic and come from orbits of certain bounded linear operators on Banach spaces. This extends the known results for nilsequences and return time sequences of the form for a measure preserving system and , avoiding in the latter case the problem of finding the full measure set of appropriate points .