向量函数空间上的连续小波变换

Continuous Wavelet Transform on the Vector Function Space

讨论了向量函数空间上的连续小波变换 ,分别得到了由变换向量函数产生的重构公式和由不同于变换向量函数的向量函数生成的重构公式 ,获得了两种重构公式在弱拓扑下和在强拓扑下成立的条件 ,并得到了一种选取变换函数使得重构公式为最简单形式的方法。

The continuous wavelet transform on the vector function space is discussed. The reconstruction formulas produced by the transform vector function and produced by the transformed vector function are obtained. The conditions that make the reconstruction formulas true in the strong topology are got. A method that we look for the transform vector function that makes the reconstruction formulas the simplest form is found.