A characterization of evolution operators

Volume 146 / 2001

Naoki Tanaka Studia Mathematica 146 (2001), 285-299 MSC: Primary 47D06; Secondary 34G10. DOI: 10.4064/sm146-3-5


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.


  • Naoki TanakaDepartment of Mathematics
    Faculty of Science
    Okayama University
    Okayama 700-8530, Japan

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