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.
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页码：843 / 858
页数：16
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