报告人：邹玉茹（深圳大学）

时间：2021年6月25日10:45开始

腾讯会议ID：805 161 431

摘要:Let M be a positive integer and q\in (1, M+1]. A q-expansion of a real number x is a sequence (c_i)=c_1c_2\cdots with each c_i\in \{0,1,\ldots, M\} such that x=\sum_{i=1}^{\infty}c_iq^{-i}. In this paper we study the set \mathcal{U}_q^j consisting of those real numbers having exactly j different q-expansions. Our main result is that for Lebesgue almost every q\in (q_{KL}, M+1), we have \dim_{H}\uu_{q}^{j}\leq \max\{0,2\dim_H\uu_q-1\} for all j\in\{2,3,\ldots\}. Here q_{KL} is the Komornik-Loreti constant. As a corollary of this result, we show that for any j\in\{2,3,\ldots\}, the function mapping q to \dim_{H}\uu_{q}^{j} is not continuous.

简介:邹玉茹，深圳大学数学与统计学院教授，毕业于华东师范大学，获理学博士学位。主要研究方向为分形几何及图像处理与分析等，在《Nonlinearity》、《J Number Theorey》、《IEEE Trans. Image Process.》、《Inverse Problems》等重要期刊发表论文20多篇。主持国家自然科学基金项目3 项，广东省自然科学基金面上项目1项。

邀请人：孔德荣

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