Fourier Orthonormal Bases of Two Dimensional Moran Measures with Four-Element Digits

被引：0
|
作者：
Chi, Zi-Chao [1 ]
Zhang, Min-Min [1 ]
机构：
[1] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China
来源：
COMPLEX ANALYSIS AND OPERATOR THEORY | 2022年 / 16卷 / 04期
基金：
中国国家自然科学基金;
关键词：
Spectral measure; Moran measure; Orthogonal basis; Fourier transform; FUGLEDES CONJECTURE; SPECTRAL PROPERTY; MOCK; SERIES;
D O I：
10.1007/s11785-022-01231-w
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Let mu({Mn}, {Dn}) be a Moran measure generated by {(M-n, D-n)}(n=1)(infinity), where M-n = [GRAPHICS] is an element of M-2(Z) is an expanding matrix and D-n = { [GRAPHICS] , [GRAPHICS] , [GRAPHICS] , [GRAPHICS] } subset of Z(2) is a finite digit set. In the present paper we will study the problem of how to determine the Hilbert space L-2(mu({Mn},{Dn})) has a Fourier basis. We first obtain a sufficient condition for this aim and give some examples to explain the theory. Moreover, we completely settle the corresponding problem if a(n) = b(n) = 1 for all n >= 1.
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页数：20
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