L~2(R~n)中MRA Parseval框架小波和它们的乘子

刻画了L~2(R~n)中具有扩展矩阵伸缩的广义低通滤波器和多尺度分析Parseval框架小波(缩写为MRA PFW).首先,研究了伪逆的尺度函数、广义的低通滤波器和MRA PFW,给出它们的一些刻画.接着,我们给出与MRA PFW相联系的几类乘子的一些刻画.最后,给出了一个例子来证明的结论.

MRA Parseval Frame Wavelets and Their Multipliers in L~2(R~n)

In this paper,we characterize all generalized low pass filters and nmltiresolution analysis(MRA) Parseval frame wavelets in L~2(R~n) with any expanding matrix dilations.At first,we study the pseudo-scaling functions,generalized low pass filters and multiresolution analysis(MRA) Parseval frame wavelets with any expanding matrices and give some important characterizations about them.Then,we describe the Parseval frame wavelet multipliers in L~2(R~n) and give an example to prove our theory.