Non-isotropic distance measures for lattice-generated sets.

Alexander Iosevich; Misha Rudnev

Publicacions Matemàtiques (2005)

  • Volume: 49, Issue: 1, page 225-247
  • ISSN: 0214-1493

Abstract

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We study distance measures for lattice-generated sets in Rd, d>=3, with respect to non-isotropic distances l-l.K, induced by smooth symmetric convex bodies K. An effective Fourier-analytic approach is developed to get sharp upper bounds for the second moment of the weighted distance measure.

How to cite

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Iosevich, Alexander, and Rudnev, Misha. "Non-isotropic distance measures for lattice-generated sets.." Publicacions Matemàtiques 49.1 (2005): 225-247. <http://eudml.org/doc/41561>.

@article{Iosevich2005,
abstract = {We study distance measures for lattice-generated sets in Rd, d&gt;=3, with respect to non-isotropic distances l-l.K, induced by smooth symmetric convex bodies K. An effective Fourier-analytic approach is developed to get sharp upper bounds for the second moment of the weighted distance measure.},
author = {Iosevich, Alexander, Rudnev, Misha},
journal = {Publicacions Matemàtiques},
keywords = {Teoría de la medida; Dominios convexos; Geometría discreta; Análisis de Fourier; lattice point distribution, mean square estimates, distance measures, homogeneous sets},
language = {eng},
number = {1},
pages = {225-247},
title = {Non-isotropic distance measures for lattice-generated sets.},
url = {http://eudml.org/doc/41561},
volume = {49},
year = {2005},
}

TY - JOUR
AU - Iosevich, Alexander
AU - Rudnev, Misha
TI - Non-isotropic distance measures for lattice-generated sets.
JO - Publicacions Matemàtiques
PY - 2005
VL - 49
IS - 1
SP - 225
EP - 247
AB - We study distance measures for lattice-generated sets in Rd, d&gt;=3, with respect to non-isotropic distances l-l.K, induced by smooth symmetric convex bodies K. An effective Fourier-analytic approach is developed to get sharp upper bounds for the second moment of the weighted distance measure.
LA - eng
KW - Teoría de la medida; Dominios convexos; Geometría discreta; Análisis de Fourier; lattice point distribution, mean square estimates, distance measures, homogeneous sets
UR - http://eudml.org/doc/41561
ER -

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