Spectrality of a class of planar self-affine measures with three-element digit sets

被引：3
|
作者：
Chen, Yan [1 ]
Dong, Xin-Han [1 ]
Zhang, Peng-Fei [2 ]
机构：
[1] Hunan Univ, Sch Math, Changsha 410082, Hunan, Peoples R China
[2] Hunan Normal Univ, Coll Math & Stat, Changsha 410081, Hunan, Peoples R China
来源：
ARCHIV DER MATHEMATIK | 2021年 / 116卷 / 03期
关键词：
Orthogonal exponential functions; Self-affine measures; Spectral measures; Non-spectral measures; PROPERTY;
D O I：
10.1007/s00013-020-01554-0
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Let mu(M,D) be the self-affine measure generated by an expanding integer matrix M is an element of M-2(Z) and an integer three-element digit set D = {(0, 0)(T), (alpha, beta)(T), (gamma, eta)(T)}. In this paper, we show that if 3 vertical bar det(M) and 3 (sic) alpha eta-beta gamma, then L-2(mu(M,D)) has an orthogonal basis of exponential functions if and only if M* u is an element of 3Z(2), where u = (eta - 2 beta, 2 alpha - gamma)(T).
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页码：327 / 334
页数：8
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