论文标题
钢化功能的多个千古平均
Multiple ergodic averages for tempered functions
论文作者
论文摘要
遵循Frantzikinakis在平均耐强野生函数的方法的方法之后，我们通过研究钢化函数的相应平均值来添加该主题，该类别还包含振荡的函数，并且通常更限制了处理。我们的主要结果是上述平均的$ l^2 $ norm限制的存在和明确表达，事实证明，这是“预期”的一个。 The main ingredients are the use of, the now classical, PET induction (introduced by Bergelson), covering a more general case, namely a "nice" class of tempered functions (developed by Chu-Frantzikinakis-Host for polynomials and Frantzikinakis for Hardy field functions) and some equidistribution results on nilmanifolds (analogous to the ones of Frantzikinakis' for the强壮的现场案例）。
Following Frantzikinakis' approach on averages for Hardy field functions of different growth, we add to the topic by studying the corresponding averages for tempered functions, a class which also contains functions that oscillate and is in general more restrictive to deal with. Our main result is the existence and the explicit expression of the $L^2$-norm limit of the aforementioned averages, which turns out, as in the Hardy field case, to be the "expected" one. The main ingredients are the use of, the now classical, PET induction (introduced by Bergelson), covering a more general case, namely a "nice" class of tempered functions (developed by Chu-Frantzikinakis-Host for polynomials and Frantzikinakis for Hardy field functions) and some equidistribution results on nilmanifolds (analogous to the ones of Frantzikinakis' for the Hardy field case).
