Exponential dichotomies and Fredholm operators
1988; American Mathematical Society; Volume: 104; Issue: 1 Linguagem: Inglês
10.1090/s0002-9939-1988-0958058-1
ISSN1088-6826
Autores Tópico(s)Holomorphic and Operator Theory
ResumoIt is shown that if the operator ( L x ) ( t ) = x ˙ ( t ) − A ( t ) x ( t ) \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 x ˙ = A ( t ) x \dot x = A\left ( t \right )x has an exponential dichotomy on both [ 0 , ∞ ) [0,\infty ) and ( − ∞ , 0 ] ( - \infty ,0] . This gives a converse to an earlier result.
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