FREIMAN THEOREM, FOURIER TRANSFORM AND ADDITIVE STRUCTURE OF MEASURES

被引：2

作者：

Iosevich, A. ^{[1
]}

Rudnev, M. ^{[2
]}

机构：

[1] Univ Missouri, Columbia, MO 65211 USA

[2] Univ Bristol, Bristol BS8 1TW, Avon, England

来源：

JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY | 2009年 / 86卷 / 01期

基金：

美国国家科学基金会; 英国工程与自然科学研究理事会;

关键词：

Fourier transform; decay estimates; ERDOS DISTANCE PROBLEM; FINITE-FIELDS; AVERAGE DECAY; SETS;

D O I：

10.1017/S1446788708000530

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We use the Freiman theorem in arithmetic combinatorics to show that if the Fourier transform of certain measures satisfies sufficiently bad estimates, then the support of the measure possesses an additive structure. The result is then discussed in light of the Falconer distance problem.

引用

页码：97 / 109

页数：13

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