Locally Lipschitz continuous integrated semigroups

Tom 167 / 2005

Naoki Tanaka Studia Mathematica 167 (2005), 1-16 MSC: Primary 47D62; Secondary 47D60. DOI: 10.4064/sm167-1-1


This paper is concerned with the problem of real characterization of locally Lipschitz continuous $(n+1)$-times integrated semigroups, where $n$ is a nonnegative integer. It is shown that a linear operator is the generator of such an integrated semigroup if and only if it is closed, its resolvent set contains all sufficiently large real numbers, and a stability condition in the spirit of the finite difference approximation theory is satisfied.


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

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