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Ergodic Series and Weighted Ergodic Theorems
发布时间: 2018-05-12     20:52   【返回上一页】 发布人:范爱华


随机数学研究中心学术报告

 

题目: Ergodic Series and Weighted Ergodic Theorems

 

报告人: 范爱华教授(华中师范大学)

 

邀请人:张余辉

 

时间:201867日(周四)下午2:30-3:30

 

地点:后主楼1220B

 

摘要:We will present some recent results on the convergence of ergodic series of the form $\sum a_n f(T^n)$. The method applies to general random series $\sum Z_n$ of dependent terms and our result applies to dilated series in harmonic analysis. One of our motivations is the study of weighted ergodic averages $N^{-1}\sum_1^N w_nf(T^n x)$. Different oscillating conditions on the weights $(w_n)$ allows us to obtain weighted ergodic theorems (Davenport sequences, Gelfond sequences, q-multiplicative sequences, Chowla sequences etc). Such studies are related to Sarnak conjecture which establish a remarkable link between dynamical systems and number theory. Results presented are taken from joint works with Christophe CUNY, Yunping JIANG, Jakub KONIECZNY, Joerg SCHMELING, Weixiao SHEN.