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《山东大学学报(理学版)》 ›› 2020, Vol. 55 ›› Issue (2): 23-32.doi: 10.6040/j.issn.1671-9352.0.2019.509

• • 上一篇    

空间中相似变换下一些自仿测度的非谱性质

秦玲   

  1. 陕西师范大学数学与信息科学学院, 陕西 西安 710119
  • 发布日期:2020-02-14
  • 作者简介:秦玲(1995— ),女,硕士研究生,研究方向为自仿测度谱理论. E-mail:2440935112@qq.com
  • 基金资助:
    国家自然科学基金资助项目(11571214)

Non-spectrality of some self-affine measures under the similarity in space

QIN Ling   

  1. College of Mathematics and Information Science, Shaanxi Normal University, Xian 710119, Shaanxi, China
  • Published:2020-02-14

摘要: 由矩阵M=diag[p1,p2,p3]和数字集D={0,e1,e2,e3}所确定的自仿测度μM,D 的谱性和非谱性经过前人的研究已经有了很多结论,这里p1,p2,p3∈Z\{0,±1},e1、e2、e3是R3上的标准正交基。对于一般的整数扩张矩阵M=[p1,p2,p3;p4,p5,p6;p7,p8,p9]和数字集D={0,e1,e2,e3},这里介绍了一种方法去处理μM,D的非谱性。作为应用,这样的一类自仿测度的非谱性质都能被确定。

关键词: 迭代函数系, 非谱测度, 正交指数系

Abstract: The spectrality or non-spectrality of the self-affine measure μM,D corresponding to matrix M=diag[p1, p2, p3] and the digit set D={0, e1, e2, e3} has had many conclusions with previous researching, where p1, p2, p3∈Z\{0, ±1}, e1, e2, e3 are the standard basis of unit column vectors in R3. For the expanding integer matrix M=[p1, p2, p3; p4, p5, p6; p7, p8, p9] and the digit set D={0, e1, e2, e3}, a method is presented here to deal with the non-spectrality of μM,D. As an application, the non-spectrality of a class of such self-affine measures are clarified.

Key words: iterated function system, non-spectral measure, orthogonal exponential

中图分类号: 

  • O174.12
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