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Weak mixing implies weak mixing of higher orders along tempered functions

Published online by Cambridge University Press:  26 February 2009

VITALY BERGELSON  and
INGER J. HÅLAND KNUTSON
VITALY BERGELSON
Affiliation:
Department of Mathematics, The Ohio State University, Columbus, OH 43210, USA (email: [email protected])
INGER J. HÅLAND KNUTSON
Affiliation:
Department of Mathematical Sciences, University of Agder, N-4604 Kristiansand, Norway (email: [email protected])
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Abstract

We extend the weakly mixing PET (polynomial ergodic theorem) obtained in Bergelson [Weakly mixing PET. Ergod. Th. & Dynam. Sys.7 (1987), 337–349] to much wider families of functions. Besides throwing new light on the question of ‘how much higher-degree mixing is hidden in weak mixing’, the obtained results also show the way to possible new extensions of the polynomial Szemerédi theorem obtained in Bergelson and Leibman [Polynomial extensions of van der Waerden’s and Szemerédi’s theorems. J. Amer. Math. Soc.9 (1996), 725–753].

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 29 , Issue 5 , October 2009 , pp. 1375 - 1416
Copyright
Copyright © Cambridge University Press 2009

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