Van der Corput sets in d
Vitaly Bergelson ; Emmanuel Lesigne
Colloquium Mathematicae, Tome 111 (2008), p. 1-49 / Harvested from The Polish Digital Mathematics Library

In this partly expository paper we study van der Corput sets in 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
EUDML-ID : urn:eudml:doc:283754
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     author = {Vitaly Bergelson and Emmanuel Lesigne},
     title = {Van der Corput sets in $$\mathbb{Z}$^{d}$
            },
     journal = {Colloquium Mathematicae},
     volume = {111},
     year = {2008},
     pages = {1-49},
     zbl = {1177.37018},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm110-1-1}
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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/