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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Cesàro summability in a linear autonomous difference equation


Author: Mihály Pituk
Journal: Proc. Amer. Math. Soc. 133 (2005), 3333-3339
MSC (2000): Primary 39A11; Secondary 34K40
Published electronically: May 4, 2005
MathSciNet review: 2161157
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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.


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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

DOI: http://dx.doi.org/10.1090/S0002-9939-05-08154-2
PII: S 0002-9939(05)08154-2
Keywords: Difference equation, Ces\`{a}ro summability, Lyapunov exponent, Laplace transform, Tauberian theorems
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
Article copyright: © Copyright 2005 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.