Linear Sequences and Weighted Ergodic Theorems

Linear Sequences and Weighted Ergodic Theorems

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....

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Main Author: Tanja Eisner
Format: Article
Language:English
Published: Hindawi Limited 2013-01-01
Series:Abstract and Applied Analysis
Online Access:http://dx.doi.org/10.1155/2013/815726
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spelling doaj-1780185982df4e02ab08ad93b8a0ad822020-11-24T20:53:45ZengHindawi LimitedAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/815726815726Linear Sequences and Weighted Ergodic TheoremsTanja Eisner0Korteweg-de Vries Institute for Mathematics, University of Amsterdam, P.O. Box 94248, 1090 GE Amsterdam, The NetherlandsWe 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 .http://dx.doi.org/10.1155/2013/815726
collection DOAJ
language English
format Article
sources DOAJ
author Tanja Eisner
spellingShingle Tanja Eisner
Linear Sequences and Weighted Ergodic Theorems
Abstract and Applied Analysis
author_facet Tanja Eisner
author_sort Tanja Eisner
title Linear Sequences and Weighted Ergodic Theorems
title_short Linear Sequences and Weighted Ergodic Theorems
title_full Linear Sequences and Weighted Ergodic Theorems
title_fullStr Linear Sequences and Weighted Ergodic Theorems
title_full_unstemmed Linear Sequences and Weighted Ergodic Theorems
title_sort linear sequences and weighted ergodic theorems
publisher Hindawi Limited
series Abstract and Applied Analysis
issn 1085-3375
1687-0409
publishDate 2013-01-01
description 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 .
url http://dx.doi.org/10.1155/2013/815726
work_keys_str_mv AT tanjaeisner linearsequencesandweightedergodictheorems
_version_ 1716796205000818688

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