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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Exponential dichotomies and Fredholm operators


Author: Kenneth J. Palmer
Journal: Proc. Amer. Math. Soc. 104 (1988), 149-156
MSC: Primary 34C11; Secondary 47A53
MathSciNet review: 958058
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Abstract: It is shown that if the operator $ \left( {Lx} \right)\left( t \right) = \dot x\left( t \right) - A\left( t \right)x\left( t \right)$ is semi-Fredholm, then the differential equation $ \dot x = A\left( t \right)x$ has an exponential dichotomy on both $ [0,\infty )$ and $ ( - \infty ,0]$. This gives a converse to an earlier result.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1988-0958058-1
PII: S 0002-9939(1988)0958058-1
Keywords: Linear system, Fredholm operator, exponential dichotomy
Article copyright: © Copyright 1988 American Mathematical Society