函数的级数与函数空间的序列化

Function Series and Seriatron of Function Spaces

本文首先回顾了级数研究的历史梗概，接着定义了一种形式级数，并在统一的框架下讨论了经典的种种收敛性及幂级数、付立叶级数和小波级数，然后从多尺度分析出发，研究了可序列化的函数空间，得到了若干性质．

In this paper, the history of series research is first recalled,then a kind of formal series is defined some kinds of clsssical convergence conceptions, poqerseries. Fourier series and qavelet series are also discussed. At last, the serialised function spaces is studied and some their properties are obtained, starting from multi-criterion analysis.