三个数字集生成的自相似测度的乘积谱  

Multiple Spectra of Self-Similar Measures with Three Digits

作　　者：李海雄 吴新林 丁道新 Li Haixiong;Wu Xinlin;Ding Daoxing(School of Mathematics and Economics&Bigdata Modeling and Intelligent Computing Institute,Hubei University of Education,Wuhan 430205)

机构地区：[1]湖北第二师范学院数学与经济学院&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：《数学物理学报（A辑）》2022年第3期705-715,共11页Acta Mathematica Scientia

基　　金：国家自然科学基金(11401189);湖北省自然科学基金(2019CFB782)~~。

摘　　要：该文研究了自相似测度μka,b(·)=1/3∑i=0^(2)μk,,a,b(3k(·)-ki)的谱特征值问题,利用整数同余及有限乘法群元素阶的相关性质,得到了集合p∧(3k,C)={c∑_(j=0)^(finite)(3k)^jCj:Cj∈C={0,1,2)为自相似测度μk,a,b乘积谐的几个充分条件,最后通过个具体的例子来应用文中的结果.It is well known that the self-similar measureμka,b defined byμka,b(·)=1/3∑i=0^(2)μk,,a,b(3k(·)-ki)is a spectral measure with a spectrum p∧(3k,C)={c∑_(j=0)^(finite)(3k)^jCj:Cj∈C={0,1,2)In this paper,by applying the properties of congruences and the order of elements in the finite group,we obtain some conditions on the integer p such that the set p∧(3k,C)is also a spectrum forμ;.Moreover,an example is given to explain our theory.

关 键 词：自相似测度 谱测度 谱特征值 乘积谱 

分 类 号：O174.2[理学—数学]