Fourier transform and expanding maps on Cantor sets

IF 1.7 1区数学 Q1 MATHEMATICS

American Journal of Mathematics Pub Date : 2024-07-17 DOI:10.1353/ajm.2024.a932433

Tuomas Sahlsten, Connor Stevens

引用次数: 0

Abstract

abstract:

We study the Fourier transforms $\widehat{\mu}(\xi)$ of non-atomic Gibbs measures $\mu$ for uniformly expanding maps $T$ of bounded distortions on $[0,1]$ or Cantor sets with strong separation. When $T$ is totally non-linear, then $\widehat{\mu}(\xi)\to 0$ at a polynomial rate as $|\xi|\to\infty$.

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康托尔集合上的傅立叶变换和展开图

摘要:我们研究了$[0,1]$或具有强分离的康托集上有界扭曲的均匀膨胀映射$T$的非原子吉布斯量$\mu$的傅立叶变换$\widehat{mu}(\xi)$。当 $T$ 是完全非线性的，那么 $\widehat\{mu}(\xi)\to 0$ 的多项式速率为 $|\xi|\to\infty$。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

American Journal of Mathematics 数学-数学

CiteScore

3.20

自引率

0.00%

发文量

审稿时长

24 months

期刊介绍： The oldest mathematics journal in the Western Hemisphere in continuous publication, the American Journal of Mathematics ranks as one of the most respected and celebrated journals in its field. Published since 1878, the Journal has earned its reputation by presenting pioneering mathematical papers. It does not specialize, but instead publishes articles of broad appeal covering the major areas of contemporary mathematics. The American Journal of Mathematics is used as a basic reference work in academic libraries, both in the United States and abroad.