کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
6415269 1335093 2009 45 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
A general Trotter-Kato formula for a class of evolution operators
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات اعداد جبر و تئوری
پیش نمایش صفحه اول مقاله
A general Trotter-Kato formula for a class of evolution operators
چکیده انگلیسی

In this article we prove new results concerning the existence and various properties of an evolution system UA+B(t,s)0⩽s⩽t⩽T generated by the sum −(A(t)+B(t)) of two linear, time-dependent and generally unbounded operators defined on time-dependent domains in a complex and separable Banach space B. In particular, writing L(B) for the algebra of all linear bounded operators on B, we can express UA+B(t,s)0⩽s⩽t⩽T as the strong limit in L(B) of a product of the holomorphic contraction semigroups generated by −A(t) and −B(t), respectively, thereby proving a product formula of the Trotter-Kato type under very general conditions which allow the domain D(A(t)+B(t)) to evolve with time provided there exists a fixed set D⊂⋂t∈[0,T]D(A(t)+B(t)) everywhere dense in B. We obtain a special case of our formula when B(t)=0, which, in effect, allows us to reconstruct UA(t,s)0⩽s⩽t⩽T very simply in terms of the semigroup generated by −A(t). We then illustrate our results by considering various examples of nonautonomous parabolic initial-boundary value problems, including one related to the theory of time-dependent singular perturbations of self-adjoint operators. We finally mention what we think remains an open problem for the corresponding equations of Schrödinger type in quantum mechanics.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Functional Analysis - Volume 257, Issue 7, 1 October 2009, Pages 2246-2290
نویسندگان
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