JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2020, Vol. 55 ›› Issue (2): 23-32.doi: 10.6040/j.issn.1671-9352.0.2019.509

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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

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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

CLC Number: 

  • O174.12
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