A characterization of evolution operators
Volume 146 / 2001
Studia Mathematica 146 (2001), 285-299
MSC: Primary 47D06; Secondary 34G10.
DOI: 10.4064/sm146-3-5
Abstract
A class of evolution operators is introduced according to the device of Kato. An evolution operator introduced here provides a classical solution of the linear equation $u'(t)=A(t)u(t)$ for $t\in [0,T]$, in a general Banach space. The paper presents a necessary and sufficient condition for the existence and uniqueness of such an evolution operator.
