Fourier dimension and avoidance of linear patterns

：梁熠宇（北京交通大学）
：2022-05-19 15:00
：腾讯会议ID：301497640（无密码）

报告人：梁熠宇（北京交通大学）

时  间：5月19日下午15:00

地  点：腾讯会议ID：301497640（无密码）

内容摘要:

The results in this talk are of two types. On one hand, we construct sets of large Fourier dimension that avoid nontrivial solutions of certain classes of linear equations. We find a Salem set of dimension 1 that contains no nontrivial solution of any of these equations. Variants of this construction can also be used to obtain Salem sets that avoid solutions of translation-invariant linear equations of other kinds, for instance, when the collection of linear equations to be avoided is uncountable or has irrational coefficients. While such constructions seem to suggest that Salem sets can avoid many configurations, our second type of results offers a counterpoint. We show that a set whose Fourier dimension exceeds 2/(v+1) cannot avoid nontrivial solutions of all equations of some particular form.

个人简介：

梁熠宇, 北京交通大学数学与统计学院副教授, 研究方向为基础数学调和分析方向。2015年6月在北京师范大学获得博士学位。2017-2018访问加拿大英属哥伦比亚大学一年。从事调和分析及其应用相关的研究工作, 至今在包括 Adv. Math., Trans. Amer. Math. Soc., Proc. Amer. Math. Soc., J. Fourier Anal. Appl. 等刊物上发表论文十余篇, 并在 Springer 数学丛书 Lecture Notes in Mathematics 上出版专著1部。

 

联系人：杨东勇