一般函数都可以写成小波级数的形式，而由多分辨分析可得到小波的稳定有效快速变换算法。
General functions may be represented as Wavelet series. A kind of stabile, efficient and fast algorithm of Wavelet transform may be gotten through multi-resolution analysis.
首先，通过对再生核的研究，给出了小波级数的部分和在跳跃间断点处的收敛性与再生核之间的关系的等价命题。
First, by studying the producing kernel, equivalent positions of the relation between the convergence of partial sums of wavelet expansions at jumping points and producing kernel are given.
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