框架多分辨分析的算子参数化

A Parameterization of Parseval Frame Multiresolution

设M是L^2(R)中的一个Parseval框架多分辨分析,φ和Ψ是对应的Parseval尺度函数和Parseval框架小波,记为<M,φ,Ψ>.含FMSW表示所有框架多分辨分析-尺度函数-框架小波构成的集合,利用满足一定交换性质的余等距算子对这个集合进行了算子参数化.

Let M be a FMRA and letΨandφbe a(normalized tight)frame wavelet and(normalized tight)frame scaling function associated with M.Denote the set of FMRAscaling-wavelet triple<M,P,Ψ>as FMSW.In this note,the set TMSW is parameterized by a set of co-isometry operators which satisfies certain commutative properties.