三个数字集生成的Moran测度的谱性研究  

Spectrality of Moran Measures with Three-Element Didit Sets

作　　者：熊婷 Xiong Ting(School of Mathematics and Statistics,Fujian Normal University,Fuzhou 350117)

机构地区：[1]福建师范大学数学与统计学院,福州350117

出　　处：《数学物理学报（A辑）》2023年第6期1814-1830,共17页Acta Mathematica Scientia

基　　金：国家自然科学基金(11971190)。

摘　　要：假设对任意的n≥1,整数p_(n)>1和D_(n)={0,a_(n),b_(n)}■Z,其中0<a_(n)<b_(n)<P_(n).该文主要研究由整数序列(pn)^(∞)_(n=1)和数字集序列(D_(n))^(∞)_(n=1)生成的Moran测度μ:δ_(p1)^(-1){0,a_(1),b_(1)}*δ_(p1)^(-1)_(p2)^(-1){0,a_(2),b_(2)}*…*δ_(p1)^(-1)_(p2)^(-1)…_(pn)^(-1){0,a_(n),b_(n)}*…的谱性质,得到当所有数字集一致有界,μ为谱测度当且仅当对任意n≥1,序列{p_(1)p_(2)…p_(n)/3gcd(a_(n),b_(n))}^(∞)_(n=1)的3因子个数各不相同且{a_(n)/gcd(a_(n),b_(n)),b_(n)/gcd(a_(n),b_(n))}≡{1,-1}(mod 3).For n≥1,let p_(n)>1 and D_(n)=[0,a_(n),b_(n)]■Z,where 0<a_(n)<b_(n)<p_(n).This paper mainly focuses on the study of the Moran measureμ:δ_(p1)^(-1){0,a_(1),b_(1)}*δ_(p1)^(-1)_(p2)^(-1){0,a_(2),b_(2)}*…*δ_(p1)^(-1)_(p2)^(-1)…_(pn)^(-1){0,a_(n),b_(n)}*…which is generated by the sequence of integers{p_(n)}^(∞)_(n=1)and the sequence of number sets{D_(n)}^(∞)_(n=1)The author shows that when all digit sets are uniformly bounded,μis a spectral measure if and only if the numbers of factors 3 in the sequence{p_(1)p_(2)…p_(n)/3gcd(a_(n),b_(n))}^(∞)_(n=1)are different from each other and{a_(n)/gcd(a_(n),b_(n)),b_(n)/gcd(a_(n),b_(n))}≡{1,-1}(mod 3)for all n≥1.

关 键 词：指数正交基 MORAN测度 谱测度 谱 

分 类 号：O174.22[理学—数学]