The Orthogonal Bases of Exponential Functions Based on Moran-Sierpinski Measures  

作　　者：Qi Rong DENG Xing Gang HE Ming Tian LI Yuan Ling YE 

机构地区：[1]School of Mathematics and Statistics,Center for Applied Mathematics of Fujian Province&Key Laboratory of Analytical Mathematics and Applications(Ministry of Education),Fujian Normal University,Fuzhou,350117,P.R.China [2]School of Mathematics and Statistics,Key Lab NAA-MOE and Hubei Key Lab-Math.Sci.,Central China Normal University,Wuhan,430079,P.R.China [3]School of Mathematical Sciences&South China Research Center for Applied Mathematics and Interdisciplinary Studies,South China Normal University,Guangzhou,510631,P.R.China

出　　处：《Acta Mathematica Sinica,English Series》2024年第7期1804-1824,共21页数学学报（英文版）

基　　金：supported by the National Natural Science Foundation of China (Grant Nos. 12371087, 11971109,11971194, 11672074 and 12271185);supported by the program for Probability and Statistics:Theory and Application (Grant No. IRTL1704);the program for Innovative Research Team in Science and Technology in Fujian Province University (Grant No. IRTSTFJ);supported by Guangdong NSFC (Grant No. 2022A1515011124)

摘　　要：Let An∈M2(ℤ)be integral matrices such that the infinite convolution of Dirac measures with equal weightsμ{A_(n),n≥1}δA_(1)^(-1)D*δA_(1)^(-1)A_(2)^(-2)D*…is a probability measure with compact support,where D={(0,0)^(t),(1,0)^(t),(0,1)^(t)}is the Sierpinski digit.We prove that there exists a setΛ⊂ℝ2 such that the family{e2πi〈λ,x〉:λ∈Λ} is an orthonormal basis of L^(2)(μ{A_(n),n≥1})if and only if 1/3(1,-1)A_(n)∈Z^(2)for n≥2 under some metric conditions on A_(n).

关 键 词：Moran-Sierpinski measures orthonormal basis of exponential functions self-affine measures spectral measures 

分 类 号：O174.12[理学—数学]