Spectrality of Sierpinski-type self-affine measures

被引：12

作者：

Lu, Zheng-Yi ^{[1
]}

Dong, Xin-Han ^{[1
]}

Liu, Zong-Sheng ^{[2
]}

机构：

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

[2] Hengyang Normal Univ, Coll Math & Stat, Hengyang 421000, Hunan, Peoples R China

来源：

JOURNAL OF FUNCTIONAL ANALYSIS | 2022年 / 282卷 / 03期

关键词：

Self-affine measure; Orthogonal basis; Spectral measure; FOURIER-SERIES; MORAN MEASURES; GASKET; CONVERGENCE; MOCK; CONJECTURE; PROPERTY;

D O I：

10.1016/j.jfa.2021.109310

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study the spectral property of a class of Sierpinski-type self-affine measures mu(M,D )(.) =1/3 Sigma(d is an element of D) mu(M, D) (M (.) - d) on R-2, where M = [GRAPHICS] . is a real upper triangular expanding matrix and D = {((0)(0)), (d1)((0)), ((d2)(d3))} is a three-element real digit set with d(1)d(3) not equal 0. A necessary and sufficient condition for mu(M,D) to be a spectral measure is established. (C) 2021 Elsevier Inc. All rights reserved.

引用

页数：31

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