L^2(R^n)中Parseval框架多分辨分析的谱

On the Spectrums of Parseval Frame Multiresolution Analyses in L^2(R^n)

对L2(Rn)中Parseval框架多分辨分析进行了研究,其伸缩算子形式为(DAf)(x)=2.f(Ax),A是实整数系数n×n矩阵,且detA=2,它的尺度函数为(φx)∈L2(Rn),得出一个集合为Parseval框架多分辨分析尺度函数的谱的充要条件,从谱的的概念,理解高维空间的Parseval框架多分辨分析.

We study Parseval frame multiresolution analyses in L^2（R^n）,with maxtrix dilations of the form （DAf）（x）= √2f（Ax）,where A is an arbitrary expanding n × n matrix with integer coefficients,such that ｜detA｜ = 2,the scaling function is ψ（x）∈L^2（R^n）, we show a necessary and sufficient conditions which a set is the spectrums of Parseval frame multiresolution analyses,it will help us understand the Parseval frame multiresolution analyses from spectrums.