Hilbert直和空间中的Riesz基与标准正交基  

Riesz basis and normal orthogonal basis in Hilbert direct sum spaces

作　　者：申鹏 张建平 张磊 SHEN Peng;ZHANG Jianping;ZHANG Lei(College of Mathematics and Computer Science,Yan’an University,Yan’an 716000,China)

机构地区：[1]延安大学数学与计算机科学学院,陕西延安716000

出　　处：《延安大学学报（自然科学版）》2023年第4期88-93,共6页Journal of Yan'an University：Natural Science Edition

基　　金：国家自然科学基金项目(11961072);陕西省自然科学基础研究计划项目(2020JM-547)。

摘　　要：框架和基的研究是小波分析理论研究的重要内容之一。在预框架算子满足一定条件下,借助算子理论方法证明了两个Riesz基的直和是它们直和空间上的Riesz基,以及这两个Riesz基的直和构成了它们直和空间上的标准正交基的充分必要条件。并在一般框架扰动条件下,研究了一个Riesz基和一个Bessel序列的扰动性质。Research on frame and basis is one of the important contents of wavelet analysis theory.In this paper,we prove that the direct sum of two Riesz bases is the Riesz basis on their direct sum space by means of operator theory under certain conditions,and that the direct sum of these two Riesz bases constitutes a necessary and sufficient condition for the normal orthogonal basis on their direct sum space,provided that the preframe operator satisfies certain conditions.Finally,under the general frame perturbation condition,the perturbation properties of a Riesz basis and a Bessel sequence are studied.

关 键 词：框架 预框架算子 酉算子 RIESZ基 标准正交基 

分 类 号：O174.2[理学—数学]