报告题目：Product-form Hadamard triples and IFS spectral self-similar measures

报 告 人：安丽想副教授（华中师范大学数学与统计学院）

报告时间：2023年12月27日  9:00-10:00

报告地点：腾讯会议（691-498-844)

报告摘要：

ABSTRACT. In a previous work by Laba and Wang, it was proved that whenever there is a Hadamard triple (N, D, L), then the associated one-dimensional self-similar measure μ_N,D generated by maps N^-1(x+d) with d∈D, is a spectral measure. In this paper, we introduce product-form digit sets for finitely many Hadamard triples (N, A_k, C_k) and prove that the associated self-similar measure μ_N,D is a spectral measure. This result allows us to show that product-form self-similar tiles are spectrl sets as long as the tiles in the group Z_N obey the Coven-Meyerowitz (T1), (T2) tiling condition. Moreover, we show that all self-similar tiles with N=p^αq are spectral sets, answering a question by Fu, He and Lau in 2015. Finally, our results allow us to offer new singular spectral measures not generated by a single Hadamard triple. Such new examples allow us to classify all spectral self-similar measures generated by four equi-contraction maps, which will appear in a forthcoming paper.

报告人简介：

安丽想，华中师范大学副教授，博士生导师，湖北省青年拔尖人才。主要研究方向：分形几何，傅里叶分析，Tile理论等。已在Adv. Math.，Trans. Amer. Math. Soc., J. Funct. Anal.等权威数学杂志发表学术论文十余篇。