Spectrality of Moran measures with four-element digit sets

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:461

Article

Tang, Min-Wei¹  Yin, Feng-Li² 

[1] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Hubei, Peoples R China

[2] Zhoukou Normal Univ, Sch Math & Stat, Zhoukou 466001, Peoples R China

关键词: Compatible pair;    Spectral measure;    Moran measure;    Spectrum;   

DOI  :  10.1016/j.jmaa.2018.01.018

来源: Elsevier

【 摘 要 】

Let SE = 1/#E Sigma(a is an element of E) delta(a) denote the uniformly discrete probability measure on a finite set E. We prove that the infinite convolution (Moran measure) mu b,{D-k} = delta(b)-1D(1) * delta(b)-2D(2) *... admits an orthonormal basis of exponential provided that {D-k}(k=1)(infinity) is a uniformly bounded sequence of 4-digit spectral sets, b = 2(l+1)q with q > 1 an odd integer, and l sufficiently large (depends on D-k). We also give some examples to illustrate the result. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

Free