关于举行范爱华教授（法国Picardie大学，华中师范大学）学术报告会的通知

报告主题: Khintchin classes of subsequences of integers

报 告人: 范爱华教授（法国Picardie大学，华中师范大学）

报告时间：2023年 2月20日（星期一）上午9:30-10:30

报告地点：四号楼318

邀 请人: 李兵教授

欢迎广大师生前往！

数学学院

2023年2月17日

报告摘要：The Khintchin class of an increasing sequence of integers {a_n} is defined as the set of those Lebesgue-integrable functions f on the circle \mathbb{T} such that the Weyl equidistribution criterion for the sequence {a_n x} holds for almost every x with f. Khinchin conjectured that for the whole set of integers \mathbb{N}, the Khintchin class is the space of all integrable functions. But it was refuted by Marstrand (1970) who even proved that not all bounded functions are included in the Khintchin class. If the Khintchin class of a set of integers is equal to L^1(\mathbb{T}), we say that the set is a Khintchin set. So, \mathbb{N} is not a Khintchin set, but {2^n} is a Khinchin set by the ergodic theorem. How to construct Khintchin sets? How to determine the Khintchin class for a given set of integers?  We can also rise the problem on any compact Abelian group. In this talk, we will present some know results and propose some random sequences which are expected to be Khintchin sets.

专家简介：范爱华教授为法国Picardie大学特级教授。师从法国科学院院士Kahane教授，曾先后入选国家杰青（B类）等多项国家级人才计划。其研究领域涉及几何测度论、调和分析、概率论与随机过程、动力系统与遍历理论，p-进分析与p-进算术动力系统等; 发表学术论文120余篇。