数字集的谱性与谱自仿测度  

Spectrality of digit sets and spectral self-affine measures

作　　者：王琦[1] 李建林[1] 

机构地区：[1]陕西师范大学数学与信息科学学院,西安710119

出　　处：《中国科学：数学》2017年第6期703-712,共10页Scientia Sinica：Mathematica

基　　金：国家自然科学基金(批准号:11571214);中央高校基本科研业务费专项基金(批准号:GK201601004和2017CBY002)资助项目

摘　　要：本文主要确定与谱自仿测度μ_(M,D)相关的数字集D的谱性.研究所涉及的谱性问题与Dutkay、Han和Jorgensen的一个猜测密切相关.此猜测表明,在一维情形下,如果μ_(M,D)是谱自仿测度,则相应的数字集D总是一个谱集.对于一个自仿测度μ_(M,D),本文获得使数字集D具有谱性的一些条件,为这个猜测的成立提供了依据.另外,本文所得的结果在某些情形下也推广许多已知的相应结果.The present paper determines the spectrality of digit set D relating to a spectral self-affine measure PM, D. This is motivated by a conjecture of Dutkay, Han and Jorgensen. The conjecture states that D is always a spectral set if μM,D is a spectral measure in the dimension n = 1. For a self-affine measure μM,D, we obtain several conditions for the digit set D to be a spectral set. The result here provides some supportive evidence for the conjecture. It also generalizes the corresponding known result in a certain case. Keywords self-afflne measure, spectrality, compatible pair, digit set

关 键 词：自仿测度 谱性 和谐对 数字集 

分 类 号：O174.12[理学—数学]