平面上两个数字集生成的一类Moran测度的谱性  

The spectrality of a class of Moran measures with two-element digit sets in the plane

作　　者：李海雄 吴新林 丁道新[1,2] LI Haixiong;WU Xinlin;DING Daoxin(School of Mathematics and Economics, Hubei University of Education, Wuhan 430205, China;Bigdata Modeling and Intelligent Computing Research Institute, Hubei University of Education, Wuhan 430205, China)

机构地区：[1]湖北第二师范学院数学与经济学院,武汉430205 [2]湖北第二师范学院大数据建模与智能计算研究所,武汉430205

出　　处：《华中师范大学学报（自然科学版）》2021年第2期171-175,共5页Journal of Central China Normal University：Natural Sciences

基　　金：国家自然科学基金青年基金项目(11401189).

摘　　要：设Mn=anbn(n≥1)为任意扩张矩阵,D=00,102.该文通过构造一维2个数字集生成Moran测度的谱,得到了Moran测度μ_(Mn,D)为谱测度的充要条件是an(n≥2)均为偶数,进一步给出了μ_(Mn,D)的一类谱的结构.Let Mn=anbn be an expanding positive integer matrix for each n≥1,and let D=00,102 be a finite digit set.In this paper,according to constructing the spectrum of the Moran measure with two-element digit sets in the line,we obtain the necessary and sufficient condition for Moran measureμ_(Mn,D) to be a spectral measure is that an(n≥2)is even.Furthermore,the structure of a kind of spectrum for the Moran measureμ_(Mn,D) is given in the end.

关 键 词：MORAN测度 指数型正交基 谱测度 谱集 

分 类 号：O174.2[理学—数学]