Spectrality of planar self-affine measures with two-element digit set

被引：0
作者：
JianLin Li
ZhiYing Wen
机构：
[1] Shaanxi Normal University,College of Mathematics and Information Science
[2] Tsinghua University,Department of Mathematical Sciences
来源：
Science China Mathematics | 2012年 / 55卷
关键词：
self-affine measure; orthogonal exponentials; spectrality; Bernoulli convolution; compatible pair; 28A80; 42C05; 46C05;
D O I：
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学科分类号：
摘要：
The iterated function system with two-element digit set is the simplest case and the most important case in the study of self-affine measures. The one-dimensional case corresponds to the Bernoulli convolution whose spectral property is understandable. The higher dimensional analogue is not known, for which two conjectures about the spectrality and the non-spectrality remain open. In the present paper, we consider the spectrality and non-spectrality of planar self-affine measures with two-element digit set. We give a method to deal with the two-dimensional case, and clarify the spectrality and non-spectrality of a class of planar self-affine measures. The result here provides some supportive evidence to the two related conjectures.
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页码：593 / 605
页数：12
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