高维周期尺度函数的双正交性

Biorthogonality of multidimensional periodic scaling functions

利用转移算子和一致可积性的有关知识 ,讨论了周期小波分析中高维周期尺度函数的双正交性 ,得到了尺度函数双正交的充要条件 .所得结果推广了尺度函数正交性的某些结果 ,在周期小波分析理论及应用的研究中 。

The concept of wavelet was first put forward in 1984.In about 1986,Y.Meyer,happened to construct a real wavelet basis with mathematical method,and soon after that he and S.Mallat established usual method to construct wavelet,Multiresolution Analysis.Since then wavelets analysis has become a kind of science and developed rapidly.Especially,Since I.Daubechies constructed compactly supported orthonormal wavelet in 1988,the research of wavelets analysis and its application have drawn close attention of scholars of various academic fields from all over the world.The application,influence and development of wavelet analysis is unprecedented,and its success is worth notice. In this paper,we discuss biorthogonality of multidimensional periodic scaling functions.Especially,we give a necessary and sufficient condition for biorthogonality of periodic scaling functions which are defined by a family filters.It is very important for us to study the theory and application of periodic wavelets analysis.