广州数学大讲坛第三期
第二十九讲——芬兰奥卢大学伍智义研究员学术报告
题目：Some facts in fractal spectral theory
时间：2022年6月16（周四）下午14：30-16：30
地点：腾讯会议（会议ID：233 187 162)
报告人：伍智义研究员
摘要：Fractal spectral measure theory is a field connecting fractal geometry and Fourier analysis. More specifically, it is about the existence and structure of the exponential orthonormal bases on fractal measures. In this talk, I will introduce some facts about it. Specifically, I will give the proofs of the next three facts about the standard fourth-middle Cantor measure \mu_4:
(1)\mu_4 is a spectral measure with a spectrum _4 (Jorgensen and Pederson, 1998);
(2)5\Lamda_4 is also a spectrum of \mu_4 (Laba and Wang first note that this fact in 2002);
(3)there exists a spectrum \Lamda of \mu_4 such that its Beurling dimension is zero (Dai, He and Lai, 2013).
If time permits, I will introduce the ideas of proofs about the convergence results of \mu_4 obtained by Strichartz (2006) and Dutkay et al. (2014).
报告人简介：
伍智义，博士毕业于华中师范大学，现为奥卢大学博士后、研究员，主要研究方向为分形几何和调和分析，在J. Funct. Anal.，JFAA，Nonlinearity等期刊发表论文多篇。
