一种特殊抽象函数空间上的连续小波变换  

Continuous wavelet transforms in a special abstract function space

作　　者：屈汉章[1] 韩俊刚[1] 

机构地区：[1]西安邮电学院数理系,陕西西安710061

出　　处：《西安电子科技大学学报》2005年第3期481-488,共8页Journal of Xidian University

基　　金：国家自然科学基金资助项目(90207015)

摘　　要：讨论了一种特殊的抽象函数空间L2(R,H),把连续小波变换从L2(R)推广到L2(R,H);讨论了由抽象变换函数的积分核产生的重构公式,不仅在弱收敛意义下而且在范数收敛意义下该重构公式成立的条件;得到了使得重构公式存在且成为最简单形式的抽象变换函数的条件;给出了一种寻求使得重构公式成为最简单形式的抽象变换函数的方法.A special abstract function L2(R,H) is discussed, the continuous wavelet transform on L2(R) is generalized to that on L2(R,H), and the reconstruct formula produced by the integral kernel of the abstract transform function is discussed. The conditions which make the reconstruction formula true not only in the weak topology but also in the strong topology are discussed. Generally speaking, there does not exist the reconstruction formula. The condition of abstract functions which makes the reconstruction formula the simplest is obtained. A method of finding the abstract functions which make the reconstruction formula the simplest is given.

关 键 词：FOURIER变换 连续小波变换 弱拓扑 强拓扑 

分 类 号：O174.22[理学—数学]