一类四元素数字集的正交函数的个数  

The cardinality of a class of orthogonal exponential function with four-element digit set

作　　者：周脉东[1,2] 

机构地区：[1]陕西师范大学数学与信息科学学院,陕西西安710062 [2]陕西教育学院数学系,陕西西安710061

出　　处：《纯粹数学与应用数学》2012年第1期80-84,共5页Pure and Applied Mathematics

基　　金：陕西省科学技术研究发展计划(二)项目(2011JE002)

摘　　要：自仿测度的谱与非谱问题近年引起了很大的关注,关于自仿测度的非谱问题,其中之一就是要估算它在L2空间上的正交指数的个数.通过对μM,D傅里叶变换的零点集性质的分析和讨论,对现有的结论进行了改进,确定了相应四元素数字集的平面自仿测度在L2的空间上正交指数函数的最大个数为3.The problem of the spectrality or non-spectrality of a self-affine measure have been received much attention in recent years. One of non-spectrality problem on a self-affine measure is to estimate the number of orthogonal exponentials in Lu. By the analysis of characterization of the zero set of the Fourier transform of μM,D, Improve the result and get the biggest number of the orthogonal exponential functions of planar self-affine measure with four-elements digit set for the L2 space is 3.

关 键 词：自仿测度 谱测度 正交指数函数 迭代函数系 

分 类 号：O174.12[理学—数学]