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Themth difference operator applied toL2functions on a finite interval

Authors
Journal
Linear Algebra and its Applications
0024-3795
Publisher
Elsevier
Publication Date
Volume
366
Identifiers
DOI: 10.1016/s0024-3795(02)00470-6
Keywords
  • Difference Operator
  • Spectral Analysis
  • Toeplitz Matrix
  • Chopping And Nodding

Abstract

Abstract 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.

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