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Convergence of Conze–Lesigne averages

Published online by Cambridge University Press:  30 March 2001

BERNARD HOST  and
BRYNA KRA
BERNARD HOST
Affiliation:
Equipe d'analyse et de mathématiques appliquées, Université de Marne la Vallée, 77454 Marne la Vallée Cedex, France (e-mail: {host,kra}@math.univ-mlv.fr)
BRYNA KRA
Affiliation:
Equipe d'analyse et de mathématiques appliquées, Université de Marne la Vallée, 77454 Marne la Vallée Cedex, France (e-mail: {host,kra}@math.univ-mlv.fr)
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Abstract

We study the convergence of N^{-1} \sum f_1(T^{a_1n}x)f_2(T^{a_2n}x)f_3(T^{a_3n}x), for a measure-preserving system (X, \mathcal{B}, \mu, T) and f_{1}, f_{2}, f_{3} \in L^{\infty}(\mu). This generalizes the theorem of Conze and Lesigne on such expressions and simplifies the proof. We also obtain a description of the limit.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 21 , Issue 2 , April 2001 , pp. 493 - 509
Copyright
2001 Cambridge University Press

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