FOURIER DECAY OF SELF-SIMILAR MEASURES AND SELF-SIMILAR SETS OF UNIQUENESS

被引：7

作者：

Varju, Peter P. ^{[1
]}

Yu, Han ^{[1
]}

机构：

[1] Univ Cambridge, Ctr Math Sci, Cambridge, England

来源：

ANALYSIS & PDE | 2022年 / 15卷 / 03期

基金：

欧洲研究理事会;

关键词：

Rajchman measure; Fourier decay of self-similar measures; sets of uniqueness; digit changes;

D O I：

10.2140/apde.2022.15.843

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We investigate the Fourier transform of self-similar measures on R. We provide quantitative decay rates of Fourier transform of some self-similar measures. Our method is based on random walks on lattices and Diophantine approximation in number fields. We also completely identify all self-similar sets which are sets of uniqueness. This generalizes a classical result of Salem and Zygmund.

引用

页码：843 / 858

页数：16

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