Cesàro summability in a linear autonomous difference equation

Pituk, Mihály

doi:10.1090/S0002-9939-05-08154-2

Cesàro summability in a linear autonomous difference equation
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by Mihály Pituk PDF

Proc. Amer. Math. Soc. 133 (2005), 3333-3339 Request permission

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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