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Van der Corput sets in Z^d

By Vitaly Bergelson and Emmanuel Lesigne


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 in [Kam-MF] and [Ruz], 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

Topics: sequences
Year: 2007
OAI identifier: oai:CiteSeerX.psu:
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