The Spectrality of a Class of Fractal Measures on R^(n)  

作　　者：Jing Cheng LIU Zhi Yong WANG Yao LIU Ya SHI 

机构地区：[1]Key Laboratory of Computing and Stochastic Mathematics(Ministry of Education),School of Mathematics and Statistics,Hunan Normal University,Changsha 410081,P.R.China [2]School of Mathematics and Statistics,Hunan First Normal University,Changsha 410205,P.R.China

出　　处：《Acta Mathematica Sinica,English Series》2023年第5期952-966,共15页数学学报（英文版）

基　　金：Supported by the NNSF of China(Grant Nos.12071125,12001183 and 11831007);the Hunan Provincial NSF(Grant Nos.2020JJ5097 and 2019JJ20012);the SRF of Hunan Provincial Education Department(Grant No.19B117)。

摘　　要：Let M=ρ^(-1)I∈Mn(R)be an expanding matrix with 0<|ρ|<1 and D■Z^(n)be a finite digit set with O∈D and Z(mD)■Z(mD)■Z(mD)∪{0}■m^(-1)z^(n)for a prime m,where Z(mD):=(Ede emi(a)=O),LetμM.D be theassociatedsel-simiar measure defined by M.DO)-ZaeDμM,D(M()-d).In this paper,the necessary and sufficient conditions for L2(μM,D)to admit infinite orthogonal exponential functions are given.Moreover,by using the order theory of polynomial,we estimate the number of orthogonal exponential functions for all cases that L^(2)(μM,D)does not admit infinite orthogonal exponential functions.

关 键 词：Fractal spectral measure orthogonal exponentials Fourier transform SPECTRUM 

分 类 号：O174.12[理学—数学]