Analysis of two step nilsequences

Details Analysis of two step nilsequences Analysis of two step nilsequences

2007-09-20

arxiv.org/abs/0709.3241v1

Mathematics

Dynamical Systems

Scientific paper

Nilsequences arose in the study of the multiple ergodic averages associated to Furstenberg's proof of Szemer\'edi'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 2-step nilsequences and give a classification scheme for them.

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