Analysis of two step nilsequences

Bernard Host[1]; Bryna Kra[2]

  • [1] Université Paris-Est Laboratoire d’analyse et de mathématiques appliquées UMR CNRS 8050, 5 bd Descartes 77454 Marne la Vallée Cedex 2 (France)
  • [2] Department of Mathematics Northwestern University 2033 Sheridan Road, Evanston IL 60208-2730 (USA)

Annales de l’institut Fourier (2008)

  • Volume: 58, Issue: 5, page 1407-1453
  • ISSN: 0373-0956

Abstract

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Nilsequences arose in the study of the multiple ergodic averages associated to Furstenberg’s proof of Szemerédi’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.

How to cite

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Host, Bernard, and Kra, Bryna. "Analysis of two step nilsequences." Annales de l’institut Fourier 58.5 (2008): 1407-1453. <http://eudml.org/doc/10353>.

@article{Host2008,
abstract = {Nilsequences arose in the study of the multiple ergodic averages associated to Furstenberg’s proof of Szemerédi’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.},
affiliation = {Université Paris-Est Laboratoire d’analyse et de mathématiques appliquées UMR CNRS 8050, 5 bd Descartes 77454 Marne la Vallée Cedex 2 (France); Department of Mathematics Northwestern University 2033 Sheridan Road, Evanston IL 60208-2730 (USA)},
author = {Host, Bernard, Kra, Bryna},
journal = {Annales de l’institut Fourier},
keywords = {Nilsequence; nilmanifold; almost periodic sequence; nilsequence},
language = {eng},
number = {5},
pages = {1407-1453},
publisher = {Association des Annales de l’institut Fourier},
title = {Analysis of two step nilsequences},
url = {http://eudml.org/doc/10353},
volume = {58},
year = {2008},
}

TY - JOUR
AU - Host, Bernard
AU - Kra, Bryna
TI - Analysis of two step nilsequences
JO - Annales de l’institut Fourier
PY - 2008
PB - Association des Annales de l’institut Fourier
VL - 58
IS - 5
SP - 1407
EP - 1453
AB - Nilsequences arose in the study of the multiple ergodic averages associated to Furstenberg’s proof of Szemerédi’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.
LA - eng
KW - Nilsequence; nilmanifold; almost periodic sequence; nilsequence
UR - http://eudml.org/doc/10353
ER -

References

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