کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
9501780 | 1338787 | 2005 | 42 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Fredholm differential operators with unbounded coefficients
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
آنالیز ریاضی
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چکیده انگلیسی
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 Râ 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 uâ²(t)=A(t)u(t) with, generally, unbounded operators A(t),tâR, the operator G is a closure of the operator âddt+A(t). Thus, this paper provides a complete infinite-dimensional generalization of well-known finite-dimensional results by Palmer, and by Ben-Artzi and Gohberg.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Differential Equations - Volume 208, Issue 2, 15 January 2005, Pages 388-429
Journal: Journal of Differential Equations - Volume 208, Issue 2, 15 January 2005, Pages 388-429
نویسندگان
Yuri Latushkin, Yuri Tomilov,