A class of spectral self-affine measures with four-element digit sets

被引：12
|
作者：
Yang, Ming-Shu [1 ]
Li, Jian-Lin [1 ]
机构：
[1] Shaanxi Normal Univ, Coll Math & Informat Sci, Xian 710062, Peoples R China
来源：
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2015年 / 423卷 / 01期
基金：
中国国家自然科学基金;
关键词：
Iterated function system; Self-affine measure; Spectral pair; Compatible pair; Digit set; ITERATED FUNCTION SYSTEMS; DENSE ANALYTIC SUBSPACES; MOCK FOURIER-SERIES; FRACTAL L-2-SPACES; CANTOR MEASURES;
D O I：
10.1016/j.jmaa.2014.10.004
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
The self-affine measure mu(M,D) associated with an expanding matrix M is an element of M-n(Z) and a finite digit set D subset of Z(n) is uniquely determined by the self-affine identity with equal weight. In this paper we construct a class of self-affine measures mu(M,D) with four-element digit sets in the higher dimensions (n >= 3) such that the Hilbert space L-2(mu(M,D)) possesses an orthogonal exponential basis. That is, mu(M,D) is spectral. Such a spectral measure cannot be obtained from the condition of compatible pair. This extends the corresponding result in the plane. (C) 2014 Elsevier Inc. All rights reserved.
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页码：326 / 335
页数：10
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