Van der Corput sets in $ \mathbb Z^d$
Volume 110 / 2008
Colloquium Mathematicum 110 (2008), 1-49
MSC: 11K06, 28D05, 37A45, 42A82.
DOI: 10.4064/cm110-1-1
Abstract
In this partly expository paper we study van der Corput sets in ${\mathbb Z}^d$, 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.
