Cesàro summability in a linear autonomous difference equation
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Abstract:
For a linear autonomous difference equation with a unique real eigenvalue $\lambda _{0}$, it is shown that for every solution $x$ the ratio of $x$ and the eigensolution corresponding to $\lambda _{0}$ 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 $\lambda _{0}$. The proof is based on a Tauberian theorem for the Laplace transform.References
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Additional Information
- Mihály Pituk
- Affiliation: Department of Mathematics and Computing, University of Veszprém, P. O. Box 158, 8201 Veszprém, Hungary
- Email: pitukm@almos.vein.hu
- Received by editor(s): June 21, 2004
- Published electronically: May 4, 2005
- Additional Notes: This research was supported in part by the Hungarian National Foundation for Scientific Research (OTKA) Grant No. T 046929
- Communicated by: Carmen C. Chicone
- © Copyright 2005
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 133 (2005), 3333-3339
- MSC (2000): Primary 39A11; Secondary 34K40
- DOI: https://doi.org/10.1090/S0002-9939-05-08154-2
- MathSciNet review: 2161157