Spectral property of a class of Moran measures on R

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:430

Article

Fu, Yan-Song¹  Wen, Zhi-Xiong¹ 

[1] Huazhong Univ Sci & Technol, Sch Math & Stat, Wuhan 430074, Peoples R China

关键词: Compatible pair;    Admissible pair;    Spectral measure;    Moran measure;    Convolution of measures;    Self-similar measure;   

DOI  :  10.1016/j.jmaa.2015.05.006

来源: Elsevier

【 摘 要 】

Let b >= 2 be a positive integer. Let D be a finite subset of Z and {n(k)}(k=1)(infinity) subset of N be a sequence of strictly increasing numbers. A Moran measure mu(b,D),({nk}) is a Borel probability measure generated by the Moran iterated function system (Moran IFS) {f(k,d)(x) = b(nk-1-nk)(x + d) : d is an element of D, k is an element of N, n(0) = 0}In this paper we study one of the basic problems in Fourier analysis associated with mu(b,D),({nk}). More precisely, we give some conditions under which the measure mu(b,D,{nk}). is a spectral measure, i.e., there exists a discrete subset Lambda subset of R such that E(Lambda) = {e(2 pi i lambda x) : lambda E Lambda} is an orthonormal basis for L-2((mu b,D,{nk})). (C) 2015 Elsevier Inc. All rights reserved.

【 授权许可】

Free