Non-isotropic distance measures for lattice-generated sets

A Iosevich, M Rudnev

Research output: Contribution to journalArticle (Academic Journal)peer-review

3 Citations (Scopus)

Abstract

We study distance measures for lattice-generated sets in R-d, d ≥ 3, with respect to non-isotropic distances |(.)|(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 contributionNon-isotropic distance measures for lattice-generated sets
Original languageEnglish
Pages (from-to)225 - 247
JournalPublicacions Matematiques
Volume49 (1)
Publication statusPublished - 2005

Bibliographical note

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

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