Fredholm Differential Operators with Unbounded Coefficients

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dc.creatorLatushkin, Yuri
dc.creatorTomilov, Yuri
dc.date2003-08-01
dc.date.accessioned2026-07-07T04:30:26Z
dc.date.available2026-07-07T04:30:26Z
dc.descriptionWe prove that a first order linear differential operator G with unbounded operator coefficients is Fredholm on spaces of functions on the real line with values in a reflexive Banach space if and only if the corresponding strongly continuous evolution family has exponential dichotomies on both semiaxises 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), 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.
dc.description43 pp
dc.identifierhttps://arxiv.org/abs/math-ph/0308002
dc.identifierhttp://arxiv.org/abs/math-ph/0308002
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/57464
dc.subjectMathematical Physics
dc.subjectClassical Analysis and ODEs
dc.subjectDynamical Systems
dc.subjectFunctional Analysis
dc.subject47D06; 35P05; 35F10; 58J20; 58E99; 47A53
dc.titleFredholm Differential Operators with Unbounded Coefficients
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