Van der Corput sets in Z^d

Details Van der Corput sets in Z^d Van der Corput sets in Z^d

2007-10-25

arxiv.org/abs/0710.4861v1

Mathematics

Dynamical Systems

Scientific paper

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 \cite{K-MF} and \cite{R}, 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.

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