小波框架的齐次逼近性质

文章先给出了两个Banach空间,它们中的函数对于满足一定条件的参数序列能产生小波框架,并且在参数和生成元函数有微小扰动的情况下仍然为小波框架。后在前文的基础上放宽了函数属于F1(R)的充分条件。一步,F0(R)中的生成元产生的小波框架满足强齐次逼近条件,也就是函数的小波框架展开式的逼近率在它进行伸缩平移以后是不变的。

Thesis Topic:Homogeneous Approximation Property for Wavelet Frames

This paper first introduced two Banach spaces from which functions can generate wavelet frames for every sufficiently dense sequence of wellspread time-scale parameters, and a frame generated by such a function remains a frame when the time-scale parameters and the generator subject to small perturbations. Based on the former study, a lighter sufficient condition for a function to belong to the Banach space F1(R) is given. Furthermore, wavelet frames generated by the function in F0(R) possess the Strong Homogeneous Approximation Property (Strong HAP). That is the rate of approximation of a wavelet frame expansion of a function is invariant under time-scale shifts of it.