Van der Corput sets in $ℤ^{d}$

• Autorzy: Vitaly Bergelson , Emmanuel Lesigne
• Języki publikacji: EN

Abstrakty

EN

In this partly expository paper we study van der Corput sets in $ℤ^{d}$, 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.

Kategorie tematyczne

• 11K06: General theory of distribution modulo 1
• 42A82: Positive definite functions
• 37A45: Relations with number theory and harmonic analysis
• 28D05: Measure-preserving transformations

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2008
• Tom: 110
• Numer: 1
• Strony: 1-49

Daty

wydano

2008

Twórcy

autor

Vitaly Bergelson

• Department of Mathematics, The Ohio State University, Columbus, OH 43210, U.S.A.

autor

Emmanuel Lesigne

• Laboratoire de Mathématiques, et Physique Théorique, (UMR CNRS 6083), Fédération de Recherche Denis Poisson, Université François Rabelais, Parc de Grandmont, 37200 Tours, France

Identyfikatory

DOI

10.4064/cm110-1-1