一类平面Moran测度的谱性研究  

Spectrality of a Class of Planar Moran Measures

作　　者：廖暑芃 廖冬妮[2] LIAO Shupeng;LIAO Dongni(Ganzhou No.3 Middle School;School of Mathematics and Computer Science,Gannan Normal University,Ganzhou 341000,China)

机构地区：[1]赣州市第三中学 [2]赣南师范大学数学与计算机科学学院,江西赣州341000

出　　处：《赣南师范大学学报》2024年第3期8-12,共5页Journal of Gannan Normal University

基　　金：江西省教育厅科技计划项目(GJJ2201204)。

摘　　要：谱测度的研究是经典傅里叶分析在一般测度上的推广,它对分形几何、调和分析和小波分析等领域的研究都有重要意义.文章主要研究由扩张整矩阵序列和四元标准数字集序列生成的一类平面Moran测度的谱性.通过研究测度的傅里叶变换的零点与正交集之间的关系,进一步刻画该Moran测度的谱结构.最后,给出该Moran测度成为谱测度的必要条件.The study of spectral measures is a generalization of classical Fourier analysis on general measures,and it is of great significance to fractal geometry,harmonic analysis and wavelet analysis.This paper mainly studies the spectrality of a class of planar Moran measures generated by a sequence of expanding integral matrices and a sequence of four-element standard digit sets.By studying the relationship between the zero set of the Fourier transform of the measure and the orthogonal set,the spectral structure of the Moran measure is further characterized.Finally,the necessary condition for the Moran measure to become a spectral measure is given.

关 键 词：谱测度 谱 MORAN测度 傅里叶变换 

分 类 号：O174[理学—数学]