Van der Corput sets in $ℤ^{d}$

Vitaly Bergelson; Emmanuel Lesigne

Van der Corput sets in

ℤ^{d}

Vitaly Bergelson ; Emmanuel Lesigne

Colloquium Mathematicae, Tome 111 (2008), p. 1-49 / Harvested from The Polish Digital Mathematics Library

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Résumé

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.

Publié le : 2008-01-01

Zbl 1177.37018

EUDML-ID : urn:eudml:doc:283754

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     title = {Van der Corput sets in $$\mathbb{Z}$^{d}$
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Vitaly Bergelson; Emmanuel Lesigne. Van der Corput sets in $ℤ^{d}$
            . Colloquium Mathematicae, Tome 111 (2008) pp. 1-49. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm110-1-1/