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 | References | Similar Articles | Additional Information

Abstract: For a linear autonomous difference equation with a unique real eigenvalue , it is shown that for every solution the ratio of and the eigensolution corresponding to 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 . 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

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.