数学物理学报 ›› 2023, Vol. 43 ›› Issue (6): 1814-1830.

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三个数字集生成的 Moran 测度的谱性研究

熊婷()   

  1. 福建师范大学数学与统计学院 福州 350117
  • 收稿日期:2022-11-22 修回日期:2023-04-10 出版日期:2023-12-26 发布日期:2023-11-16
  • 作者简介:熊婷,E-mail: 602855710@qq.com
  • 基金资助:
    国家自然科学基金(11971190)

Spectrality of Moran Measures with Three-Element Didit Sets

Xiong Ting()   

  1. School of Mathematics and Statistics, Fujian Normal University, Fuzhou 350117
  • Received:2022-11-22 Revised:2023-04-10 Online:2023-12-26 Published:2023-11-16
  • Supported by:
    NSFC(11971190)

摘要:

假设对任意的 n1, 整数 pn>1Dn={0,an,bn}Z, 其中 $ 0

μ:=δp11{0,a1,b1}δp11p21{0,a2,b2}δp11p21pn1{0,an,bn}

的谱性质, 得到当所有数字集一致有界时, μ 为谱测度当且仅当对任意 n1, 序列 {p1p2pn3gcd(an,bn)}n=13 因子个数各不相同且 {angcd(an,bn),bngcd(an,bn)}{1,1} (mod 3).

关键词: 指数正交基, Moran 测度, 谱测度,

Abstract:

For n1, let pn>1 and Dn={0,an,bn}Z, where $0

μ:=δp11{0,a1,b1}δp11p21{0,a2,b2}δp11p21pn1{0,an,bn}

which is generated by the sequence of integers {pn}n=1 and the sequence of number sets {Dn}n=1. The author shows that when all digit sets are uniformly bounded, μ is a spectral measure if and only if the numbers of factors 3 in the sequence {p1p2pn3gcd(an,bn)}n=1 are different from each other and {angcd(an,bn),bngcd(an,bn)}{1,1} (mod 3) for all n1.

Key words: Exponential orthogonal basis, Moran measure, Spectral measure, Spectrum

中图分类号: 

  • O174.22