Non-isotropic distance measures for lattice-generated sets

Alex Iosevich, M. Rudnev

Type: Article

Publication Date: 2005-01-01

Citations: 3

DOI: https://doi.org/10.5565/publmat_49105_11

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 Erdös-Falconer distance problem.

Locations

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+ PDF Chat	Mean lattice point discrepancy bounds, II: Convex domains in the plane	2007	Alex Iosevich Eric T. Sawyer Andreas Seeger
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Works Cited by This (16)

Action	Title	Year	Authors
+	Lectures on Harmonic Analysis	2003	Thomas Wolff
+	Vorlesungen über Zahlentheorie	1950	Helmut Hasse
+	None	1999	Thomas Wolff
+ PDF Chat	On the average order of the lattice rest of a convex body	1997	Wolfgang Müller
+	Fourier Integrals in Classical Analysis	2017	Christopher D. Sogge
+	None	2003	Alex Iosevich Mischa Rudnev
+ PDF Chat	Mean square discrepancy bounds for the number of lattice points in large convex bodies	2002	Alex Iosevich Eric T. Sawyer Andreas Seeger
+	Hausdorff dimension and distance sets	1994	Jean Bourgain
+	Spherical averages of Fourier transforms of measures with finite energy; dimensions of intersections and distance sets	1987	Pertti Mattila
+	Fourier Transforms Related to Convex Sets	1962	Carl Herz