Exponential Dichotomies and Fredholm Operators
Copyright policy )Exponential Dichotomies and Fredholm Operators
It 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.
exponential dichotomy, Perturbation theory of linear operators, Linear ordinary differential equations and systems, Growth and boundedness of solutions to ordinary differential equations, (Semi-) Fredholm operators; index theories
exponential dichotomy, Perturbation theory of linear operators, Linear ordinary differential equations and systems, Growth and boundedness of solutions to ordinary differential equations, (Semi-) Fredholm operators; index theories
selected citations These citations are derived from selected sources.This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).116 popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.Top 10% influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).Top 1% impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.Average
Citations provided by BIP!Popularity provided by BIP!