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Analysis of two step nilsequences

Abstract : Nilsequences arose in the study of the multiple ergodic averages associated to Furstenberg's proof of Szemeredi's Theorem and have since played a role in problems in additive combinatorics. Nilsequences are a generalization of almost periodic sequences and we study which portions of the classical theory for almost periodic sequences can be generalized for two step nilsequences. We state and prove basic properties for two step nilsequences and give a classification scheme for them.
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Submitted on : Tuesday, May 1, 2012 - 8:01:51 PM
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  • HAL Id : hal-00693083, version 1


Bernard Host, Bryna Kra. Analysis of two step nilsequences. Annales de l'Institut Fourier, Association des Annales de l'Institut Fourier, 2008, 58 (5), pp.1407--+. ⟨hal-00693083⟩



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