一类多维连续小波逆变换的逐点收敛性

Pointwise Convergence of a Class of Multi-dimensional Continuous Wavelet Inverse Transform

研究了多维连续小波逆变换的逐点收敛性。首先引入一类多维连续小波,这类多维连续小波变换具有高频时,小移动,低频时,大移动的特点;其次讨论了这类多维连续小波的逐点收敛性,给出了这类多维连续小波逆变换逐点收敛成立的一个充分条件。

In this work, a pointwise convergence of multi-dimensional continuous wavelet inverse transform was studied. Firstly, a kind of multi-dimensional continuous wavelet transform was introduced, which features small shift at high frequency and large shift at low frequency. Secondly, the pointwise converfence of muti-dimensional continuous wavelet was discussed, and a sufficient condition for the pointwise convergence of this multi-dimensional continuous wavelet inverse transform was given.