报告名称：Khintchin classes of subsequences of integers

报告专家：范爱华

专家所在单位：华中师范大学

报告时间：2023年3月24日下午15:00-17:00

报告地点：数统楼201会议室

专家简介：范爱华，华中师范大学及法国Picardie大学教授。1989年获法国南巴黎大学数学博士学位，师从法国科学院院士Kahane教授。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。曾先后入选国家杰青（B类）等多项国家级人才计划，发表学术论文120余篇。曾先后应邀访问香港中文大学，国立台湾大学，韩国高等研究院KIAS，日本Kyushu大学，德国Ernst Moritz Arndt大学，瑞典Lund大学，美国纽约城市大学CUNY，瑞士苏黎士高等理工大学ETH，英国Warwick大学等。

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 circleTsuch 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 integersN, 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(T), we say that the set is a Khintchin set. So,Nis 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.