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报告题目：Fourier transforms of some self-similar measures and applications

报  告  人：高翔  博士（湖北大学）

报告时间：2018年10月22日（星期一）下午16:00-17:00                

报告地点：4号楼131室

邀  请  人：熊瑛  教授

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数学学院

2018年10月19日

报告摘要：

We investigate the equidistribution problem in self-similar sets of the unit interval . 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.  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.

报告人简介：

高翔，武汉大学博士毕业，华中科技大学硕士毕业。曾访问交流于法国亚眠大学，华中师范大学，福建师范大学等高校，研究方向为度量数论、动力系统、傅里叶分析在分形中的应用，近期主要关注分形测度的傅里叶变换衰减性的研究及其在分形几何上的应用。