Cesàro summability in a linear autonomous difference equation

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5 Citations (Scopus)

Abstract

For a linear autonomous difference equation with a unique real eigenvalue λ0, it is shown that for every solution x the ratio of x and the eigensolution corresponding to λ0 is Cesàro summable to a limit which can be expressed in terms of the initial data. As a consequence, for most solutions the Lyapunov characteristic exponent is equal to λ0. The proof is based on a Tauberian theorem for the Laplace transform.

Original languageEnglish
Pages (from-to)3333-3339
Number of pages7
JournalProceedings of the American Mathematical Society
Volume133
Issue number11
DOIs
Publication statusPublished - Nov 1 2005

Keywords

  • Cesàro summability
  • Difference equation
  • Laplace transform
  • Lyapunov exponent
  • Tauberian theorems

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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