数学科学学院学术报告[2024] 018号

(高水平大学建设系列报告898号)

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

报告人：安丽想 副研究员（华中师范大学）

报告时间：4月15日15：00-16：45

报告地点：腾讯会议271 843 495

报告内容：In a previous work byŁaba and Wang, it was proved that whenever there is a Hadamard triple (N, D, L), then the associated one-dimensional self-similar measureμgenerated 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, Ak, Lk) by putting each triple into different scales of N. Our main result is to prove that the associated self-similar measureμis a spectral measure. This result allows us to show that product form self-similar tiles are spectral 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.

报告人简历：安丽想，华中师范大学副研究员，博士生导师。主持国家自然科学基金青年项目、面上项目各一项。研究方向是分形上的傅里叶分析，长期致力于谱测度、Tile理论及相关问题的研究。

欢迎师生参加！

报告邀请人： 邹玉茹

数学科学学院

2024年4月15日