Hilbert空间中框架,Riesz基与正交基之间的关系  

The Relationship among Frames, Riesz Bases and Orthonormal Bases in Hilbert Space

作　　者：牛晓芳[1] 李建华[2] 

机构地区：[1]陕西师范大学数学与信息科学学院,陕西西安710062 [2]河西学院数学系,甘肃张掖734000

出　　处：《河西学院学报》2007年第5期12-18,共7页Journal of Hexi University

摘　　要：本文讨论了Hilbert空间中的框架、Riesz基与正交基的关系.结果表明:无冗余的紧框架即为正交基组;Riesz基是线性无关的框架.并构造了适当的反例说明线性无关的框架不一定是无冗余的框架,正交基不一定都能构成框架.Frame in Hilbert space is one of basic concepts in wavelet analysis. It can be regarded as generalized from the concept of base, so there are close links between frames and bases in Hilbert space, especially between tight frame and orthonormal base. Also there are tight links between Riesz bases and frames. This paper discusses their relationships and concludes that exact tight flame is orthonormal basis, Riesz basis is linear independent frame.

关 键 词：HILBERT空间 Rieaz基 小波 紧框架 正交基 

分 类 号：O174[理学—数学]