Van der Corput sets in ${\mathbb{Z}}^d$

Vitaly Bergelson, and Emmanuel Lesigne. "Van der Corput sets in $ℤ^{d}$." Colloquium Mathematicae 110.1 (2008): 1-49. <http://eudml.org/doc/283754>.

@article{VitalyBergelson2008,
abstract = {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.},
author = {Vitaly Bergelson, Emmanuel Lesigne},
journal = {Colloquium Mathematicae},
keywords = {van der Corput set; set of recurrence; intersective set; uniform distribution; positive definite sequence; continuity of measure},
language = {eng},
number = {1},
pages = {1-49},
title = {Van der Corput sets in $ℤ^\{d\}$},
url = {http://eudml.org/doc/283754},
volume = {110},
year = {2008},
}

TY - JOUR
AU - Vitaly Bergelson
AU - Emmanuel Lesigne
TI - Van der Corput sets in $ℤ^{d}$
JO - Colloquium Mathematicae
PY - 2008
VL - 110
IS - 1
SP - 1
EP - 49
AB - 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.
LA - eng
KW - van der Corput set; set of recurrence; intersective set; uniform distribution; positive definite sequence; continuity of measure
UR - http://eudml.org/doc/283754
ER -