Exponential dichotomy and dichotomy radius for difference equations |
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Authors: | Adina Lumini?a Sasu |
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Affiliation: | Department of Mathematics, Faculty of Mathematics and Computer Science, West University of Timi?oara, 4 Bd. Pârvan, 300223 Timi?oara, Romania |
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Abstract: | The aim of this paper is to provide a new approach concerning the characterization of exponential dichotomy of difference equations by means of admissible pair of sequence spaces. We classify the classes of input and output spaces, respectively, and deduce necessary and sufficient conditions for exponential dichotomy applicable for a large variety of systems. By an example we show that the obtained results are the most general in this topic. As an application we deduce a general lower bound for the dichotomy radius of difference equations in terms of input-output operators acting on sequence spaces which are invariant under translations. |
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Keywords: | Difference equation Exponential dichotomy Sequence spaces Dichotomy radius |
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