Exponential dichotomies and Fredholm operators

Palmer, Kenneth J.

doi:10.1090/S0002-9939-1988-0958058-1

Exponential dichotomies and Fredholm operators
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by Kenneth J. Palmer PDF

Proc. Amer. Math. Soc. 104 (1988), 149-156 Request permission

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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