| On Polynomial Dichotomy of Linear Discrete-Time Systems in Banach Spaces |
| Received:September 15, 2014 Revised:March 09, 2015 |
| Key Words:
linear discrete-time systems uniform polynomial dichotomy polynomial dichotomy
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| Fund Project:Supported by the Fundamental Research Funds for the Central Universities (Grant No.2012LWB53) and the Natural Science Foundation of Hubei Province (Grant No.2014CFB629). |
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| Abstract: |
| This paper deals with two concepts of polynomial dichotomy for linear difference equations which are defined in a Banach space and whose norms can increase not faster than exponentially. Some illustrating examples clarify the relations between these concepts. Our approach is based on the extension of techniques for exponential dichotomy to the case of polynomial dichotomy. The obtained results are generalizations of well-known theorems about the exponential stability and exponential dichotomy. |
| Citation: |
| DOI:10.3770/j.issn:2095-2651.2015.05.007 |
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