Trigonometric multiplicative chaos and applications to random distributions  

作　　者：Aihua Fan Yves Meyer 

机构地区：[1]School of Mathematics and Statistics,Central China Normal University,Wuhan 430079,China [2]LAMFA,CNRSUMR7352,University of Picardie,Amiens 80039,France [3]CMLA,ENS-Cachan,CNRS,Universityof Paris-Saclay,Paris 91190,France

出　　处：《Science China Mathematics》2023年第1期3-36,共34页中国科学：数学（英文版）

基　　金：supported by National Natural Science Foundation of China (Grant No.11971192)。

摘　　要：The random trigonometric series∑∞n=1ρn cos(nt+ωn)on the circle T are studied under the conditions∑|ρn|^(2)=∞andρn→0,where{ωn}are independent and uniformly distributed random variables on T.They are almost surely not Fourier-Stieltjes series but determine pseudo-functions.This leads us to develop the theory of trigonometric multiplicative chaos,which produces a class of random measures.The kernel and the image of chaotic operators are fully studied and the dimensions of chaotic measures are exactly computed.The behavior of the partial sums of the above series is proved to be multifractal.Our theory holds on the torus Tdof dimension d≥1.

关 键 词：multiplicative chaos random Fourier series Hausdorff dimension Riesz potential 

分 类 号：O17[理学—数学]