一类平面Moran测度的谱性研究

Spectrality of a Class of Planar Moran Measures

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.