Spectral properties of self-similar measures with product-form digit sets

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:473

Article

Liu, Jing-Cheng¹  Peng, Rong-Gui¹  Wu, Hai-Hua² 

[1] Hunan Normal Univ, Sch Math & Stast, Key Lab Comp & Stochast Math, Minist Educ, Changsha 410081, Hunan, Peoples R China

[2] Hunan Univ, Coll Math & Econometr, Changsha 410082, Hunan, Peoples R China

关键词: Iterated function system;    Self-affine measure;    Spectral measure;    Translational tile;   

DOI  :  10.1016/j.jmaa.2018.12.062

来源: Elsevier

【 摘 要 】

In this paper, we consider the spectral properties of self-similar measures mu(R,D) generated by the integer R = N-q and the product-form digit set D = {0, 1, . . . ,N - 1}circle plus N-P {0, 1, . . . , N - 1}, where the integers q, p >= 1 and N >= 2. We show that mu(R,D) is a spectral measure if and only if q inverted iota p. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

Free