武汉大学博士高翔学术报告11月11日下午
发布时间: 2017-11-10 访问次数: 13

报告题目Equidistribution phenomenon in some self-similar sets

  

报告时间20171111日(星期六)14:30-15:15

  

报告地点:理工北楼601

  

主办:数学与信息学院

  

报告人:高翔

  

报告人简介:高翔,武汉大学博士。

  

报告摘要Equidistribution phenomenon is prevalent not just in the theory of harmonic analysis and Diophantinea pproximation, but also in dynamical systems and number theory. In this talk, we investigate the equidistribution problem in fractal subset of the unit interval (some self-similar sets). By analytic approach we show the explicit decay rate of the Fourier transforms of corresponding self-similar measures with the uniform contractive ratio. This result generalizes the Kershner and Befelov-Solomyak's theorem. We also prove that the decay rate of them under smooth enough transformation is polynomial no matter what the arithmetic property of the contractive ratio is.This generalizes the Kaufman's results, and answers the problem of Hochman and Shmerkin. As an application we give some results on equidistribution problems in self-similar sets, in particular, we extend some results of Borel ,Cassels, Schimdt on normal numbers.