【作者】 张宇；

【导师】 李建林；

【作者基本信息】 陕西师范大学 ， 基础数学， 2012， 硕士

【摘要】 本文讨论了和谐对的性质与Bernoulli迭代函数系的正交指数函数两个内容,分为三部分,设M为扩张矩阵,D是有限集,自仿测度μM.D是由迭代函数系唯一确定的,并且人(M,S)被定义为：论文的要点及主要内容如下：第一章,我们主要介绍了一些相关基本概念和引理,以及该方向国内外的研究现状和主要成果.第二章,首先讨论了和谐对与整自仿tile及谱测度的关系,推广了和谐对与整自仿tile的性质.其次,研究和谐对与谱对的关系,推广了谱对的性质,最后,给出了和谐对条件下,谱对成立的条件,对Li[4]中(μM,DΛ(M,S))是谱对的充要条件进行了适当的补充.第三章,研究了Bernoulli迭代函数系的正交指数函数,考虑了λ∈(三,1)nQ的1/2情况,特别是,由集合Λk组成的并集能否形成一类更大的正交集.更多还原

【Abstract】 In this paper, we study and investigate the properties of the compatible pair and the orthogonal exponentials for Bernoulli iterated function systems. Let M be an expanding integer matrix, D be a finite sets, μM,D is a self-affine measure associates with iterated function system and A(M, S) is defined by The key points and the main contents of this paper are as follow:In Chapter one, we mainly introduce some elementary concepts and corollaries, accordingly, some present research and results are described.In Chapter two, the properties of the compatible pair are discussed. Firstly, we study the relations of the compatible pair, the integral self-affine tile and the compatible pair, the integral self-affine tile and the spectral pair, respectively, explore the properties of the compatible pair and the integral self-affine tile.Furthermore,the relations between the compatible pair and the spectral pair are discussed. Finally, we obtain a necessary and sufficient condition for (μM,D, A(M, S)) to be a spectral pair. Condition of a spectral pair is given and some existing results are given.In Chapter three, we investigate the orthogonal exponentials for Bernoulli iterated function systems when λ=(1/2,1)∩Q. Especially, the question whether some of these Ak sets can be combined to form larger collections of orthogonal exponentials is discussed.更多还原