The cardinality of orthogonal exponentials of planar self-affine measures with three-element digit sets

被引：19
|
作者：
Chen, Ming-Liang [1 ]
Liu, Jing-Cheng [1 ]
机构：
[1] Hunan Normal Univ, Coll Math & Stat, Key Lab High Performance Comp & Stochast Informat, Minist Educ China, Changsha 410081, Hunan, Peoples R China
来源：
JOURNAL OF FUNCTIONAL ANALYSIS | 2019年 / 277卷 / 01期
关键词：
Orthogonal exponential; Self-affine measure; Spectral measure; Zeros; NON-SPECTRAL PROBLEM; PROPERTY;
D O I：
10.1016/j.jfa.2018.11.012
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper, we consider the planar self-affine measures mu(M,D) generated by an expanding matrix M is an element of M-2(Z) and an integer digit set D = {((0)(0)), ((alpha 1)(alpha 2)), ((beta 1)(beta 2))} with alpha(1)beta(2) - alpha(2)beta(1) not equal 0. We show that if det(M) is not an element of 3Z, then the mutually orthogonal exponential functions in L-2(mu(M,D)) is finite, and the exact maximal cardinality is given. (C) 2018 Elsevier Inc. All rights reserved.
引用
收藏
页码：135 / 156
页数：22
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