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Fredholm differential operators with unbounded coefficients (2008).
| Content Provider | CiteSeerX |
|---|---|
| Author | Latushkin, Yuri Tomilov, Yuri |
| Abstract | We prove that a first order linear differential operator G with unbounded operator coefficients is Fredholm on spaces of functions on R with values in a reflexive Banach space if and only if the corresponding strongly continuous evolution family has exponential dichotomies on both R+ and R − and a pair of the ranges of the dichotomy projections is Fredholm, and that the Fredholm index of G is equal to the Fredholm index of the pair. The operator G is the generator of the evolution semigroup associated with the evolution family. In the case when the evolution family is the propagator of a well-posed differential equation u ′(t) = A(t)u(t) with, generally, unbounded operators A(t),t ∈ R, the operator G is a closure of the operator − d dt +A(t). Thus, this paper provides a complete infinite dimensional generalization of well-known finite dimensional results by K. Palmer, and by A. Ben-Artzi and I. Gohberg. |
| File Format | |
| Publisher Date | 2008-01-01 |
| Access Restriction | Open |
| Subject Keyword | Unbounded Coefficient Fredholm Differential Operator Evolution Family Fredholm Index Reflexive Banach Space First Order Linear Differential Operator Unbounded Operator Coefficient Well-posed Differential Equation Evolution Semigroup Continuous Evolution Family Complete Infinite Dimensional Generalization Dichotomy Projection Exponential Dichotomy Well-known Finite Dimensional Result |
| Content Type | Text |
| Resource Type | Article |
