The mth difference operator applied to L2 functions on a finite interval

被引：2

作者：

Di Benedetto, F ^{[1
]}

机构：

[1] Univ Genoa, Dipartimento Matemat, I-16146 Genoa, Italy

来源：

LINEAR ALGEBRA AND ITS APPLICATIONS | 2003年 / 366卷

关键词：

difference operator; spectral analysis; Toeplitz matrix; chopping and nodding;

D O I：

10.1016/S0024-3795(02)00470-6

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Continuous and discrete versions of difference operators are introduced, involving special examples of Toeplitz matrices. A spectral analysis of the continuous operator is performed, providing a full characterization of the null space and the singular system. The same analysis is performed for the discrete operator under a simplifying assumption involving the discretization parameter, by showing that the singular value decomposition is preserved in some sense. Many correspondences are shown to be lost in the case where the simplifying assumption is not verified. (C) 2002 Elsevier Science Inc. All rights reserved.

引用

页码：173 / 198

页数：26