【作者】 王娟；

【导师】 李登峰；

【作者基本信息】 河南大学 ， 应用数学， 2011， 硕士

【摘要】 1952年Duffin和scheeffer首次引入了Hilbert空问上框架的概念框架类似于基却又小同于基,起初框架理论并没有得到发展，但自从小波分析诞生以后，人们才对它广泛关注，此时框架理论才得以迅速发展，目前框架理论已经广泛应用于数学、工程技术、物理学等领域，特别在信号处理、通信、图像处理等方面部有着重要的作用本学位论文主要足对框架冗余函数性质的研究.全文由四部分组成第‘章介绍框架理论的发展历程第二章给出全文用到的‘些基本概念、事实及定理第三章探讨无限维Hilbert空问上冗余函数性质第四章研究有限维Ⅲlbert空问上冗余函数性质更多还原

【Abstract】 The concept of frame in Hilbert space was introduced by Du?n and Schae?er in1952. The frame is resemble with the basis while it is di?erent from the basis. Initiallyframe did not be developed well until wavelet analysis appearance. Nowdays frame hasbeen extensively applied in mathematics, engineering technology and physics, especiallyin signal processing, communication and image processing.Some properties of redundancy function are studied in the thesis. The thesis makesup of four chapters.Chapter 1 brie?y introduces the development on frame.Chapter 2 mostly presents some basic conceptions, the facts and theorems which areused throughout the paper.Chapter 3 investigates the properties of redundancy function in the infinite dimensionHilbert space.Chapter 4 studies the properties of redundancy function in the finite dimensionHilbert space.更多还原