Non-isotropic distance measures for lattice-generated sets

A Iosevich; M Rudnev

Non-isotropic distance measures for lattice-generated sets

A Iosevich, M Rudnev

Research output: Contribution to journal › Article (Academic Journal) › peer-review

3 Citations (Scopus)

Abstract

We study distance measures for lattice-generated sets in R-d, d &GE; 3, with respect to non-isotropic distances &VERBAR;(.)&VERBAR;(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. The implications of these estimates are discussed in the context of the general Erdos-Falconer distance problem.

Translated title of the contribution	Non-isotropic distance measures for lattice-generated sets
Original language	English
Pages (from-to)	225 - 247
Journal	Publicacions Matematiques
Volume	49 (1)
Publication status	Published - 2005

Bibliographical note

Publisher: Univ Autonoma Barcelona, Dept Mathematics
Other identifier: IDS Number: 921YV

Handle.net

Persistent link

Cite this

@article{97f4d277915840c2be2b24a6870d50a6,

title = "Non-isotropic distance measures for lattice-generated sets",

abstract = "We study distance measures for lattice-generated sets in R-d, d &GE; 3, with respect to non-isotropic distances &VERBAR;(.)&VERBAR;(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. The implications of these estimates are discussed in the context of the general Erdos-Falconer distance problem.",

author = "A Iosevich and M Rudnev",

note = "Publisher: Univ Autonoma Barcelona, Dept Mathematics Other identifier: IDS Number: 921YV ",

year = "2005",

language = "English",

volume = "49 (1)",

pages = "225 -- 247",

journal = "Publicacions Matematiques",

publisher = "Universitat Autonoma de Barcelona, Seccio de Matematiques",

}

TY - JOUR

T1 - Non-isotropic distance measures for lattice-generated sets

AU - Iosevich, A

AU - Rudnev, M

N1 - Publisher: Univ Autonoma Barcelona, Dept Mathematics Other identifier: IDS Number: 921YV

PY - 2005

Y1 - 2005

N2 - We study distance measures for lattice-generated sets in R-d, d &GE; 3, with respect to non-isotropic distances &VERBAR;(.)&VERBAR;(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. The implications of these estimates are discussed in the context of the general Erdos-Falconer distance problem.

AB - We study distance measures for lattice-generated sets in R-d, d &GE; 3, with respect to non-isotropic distances &VERBAR;(.)&VERBAR;(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. The implications of these estimates are discussed in the context of the general Erdos-Falconer distance problem.

M3 - Article (Academic Journal)

VL - 49 (1)

SP - 225

EP - 247

JO - Publicacions Matematiques

JF - Publicacions Matematiques

ER -

Non-isotropic distance measures for lattice-generated sets

Abstract

Bibliographical note

Handle.net

Fingerprint

Cite this