Geodesic
Van der Corput sets in $ \mathbb Z^d$
Vitaly Bergelson1 ; Emmanuel Lesigne2
1Department of Mathematics The Ohio State University Columbus, OH 43210, U.S.A.
2Laboratoire de Mathématiques et Physique Théorique (UMR CNRS 6083) Fédération de Recherche Denis Poisson Université François Rabelais Parc de Grandmont, 37200 Tours, France
Colloquium Mathematicum, Tome 110 (2008) no. 1, pp. 1-49
Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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In this partly expository paper we study van der Corput sets in ${\mathbb Z}^d$, with a focus on connections with harmonic analysis and recurrence properties of measure preserving dynamical systems. We prove multidimensional versions of some classical results obtained for $d=1$ by Kamae and M. Mendès France and by Ruzsa, establish new characterizations, introduce and discuss some modifications of van der Corput sets which correspond to various notions of recurrence, provide numerous examples and formulate some natural open questions.
DOI : 10.4064/cm110-1-1
Keywords: partly expository paper study van der corput sets mathbb focus connections harmonic analysis recurrence properties measure preserving dynamical systems prove multidimensional versions classical results obtained kamae mend france ruzsa establish characterizations introduce discuss modifications van der corput sets which correspond various notions recurrence provide numerous examples formulate natural questions

Vitaly Bergelson  1   ; Emmanuel Lesigne  2

1 Department of Mathematics The Ohio State University Columbus, OH 43210, U.S.A.
2 Laboratoire de Mathématiques et Physique Théorique (UMR CNRS 6083) Fédération de Recherche Denis Poisson Université François Rabelais Parc de Grandmont, 37200 Tours, France 
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Vitaly Bergelson; Emmanuel Lesigne. Van der Corput sets in $ \mathbb 
Z^d$. Colloquium Mathematicum, Tome 110 (2008) no. 1, pp. 1-49. doi: 10.4064/cm110-1-1

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