摘要
在自仿测度谱与非谱问题的研究中,由两元素数字集确定的迭代函数系是最简单且最重要的情形.一维情况对应Bernoulli卷积,其谱与非谱问题是已知的,而高维尤其是二维情形还未完全确定.有猜想表明:平面中遗留的情形均对应于非谱自仿测度.针对这种情况,本文首先获得了判定两元素数字集所对应平面自仿测度非谱性的一类条件,并在一种条件下得到正交指数函数系中元素个数的最佳上界.其次给出了所得结果的应用,并举例说明了该类条件的有效性.
The iterated function system with two-element digit set is the simplest case and the most important case in the study of spectrality or non-spectrality of selfaffine measures.The one-dimensional case corresponds to the Bernoulli convolution whose spectral property is understandable.However,the higher dimensional analogue,especially the two-dimensional case has not been solved completely.Also,there is a conjecture to illustrate that in the plane,the remaining cases correspond to nonspectrality of self-affine measures.Motivated by this problem,we provide in this paper some non-spectral conditions for the planar self-affine measures with two-element digit set.Under one of the conditions,we determine the maximal cardinality of orthogonal exponentials.An application of this result and the validity of the conditions are also presented.
作者
常焕
李建林
王琦
Huan CHANG;Jian Lin LI;Qi WANG(School of Mathematics and Statistics,Shaanxi Normal University,Xi'an 710119,P.R.China;School of Arts and Sciences,Shaanxi University of Science&Technology,Xi'an 710021,P.R.China)
出处
《数学学报（中文版）》
CSCD
北大核心
2022年第1期161-170,共10页
Acta Mathematica Sinica：Chinese Series
基金
国家自然科学基金(11571214,12001346)
陕西省自然科学基础研究计划资助(2020JQ-695)。
关键词
自仿测度
正交指数函数系
非谱性
数字集
self-affine measures
orthogonal exponentials
non-spectrality
digit set
