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arXiv · 1807.05824

A Hilbert space approach to difference equations

Konrad Kitzing·Rainer Picard·Stefan Siegmund·Sascha Trostorff·Marcus Waurick
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Abstract

We consider general difference equations $u_{n+1} = F(u)_n$ for $n \in \mathbb{Z}$ on exponentially weighted $\ell_2$ spaces of two-sided Hilbert space valued sequences $u$ and discuss initial value problems. As an application of the Hilbert space approach, we characterize exponential stability of linear equations and prove a stable manifold theorem for causal nonlinear difference equations.

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Konrad Kitzing, Rainer Picard, Stefan Siegmund, Sascha Trostorff, Marcus Waurick. 2018-07-16. A Hilbert space approach to difference equations. https://arxiv.org/abs/1807.05824

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