Locally Lipschitz continuous integrated semigroups
Volume 167 / 2005
Studia Mathematica 167 (2005), 1-16
MSC: Primary 47D62; Secondary 47D60.
DOI: 10.4064/sm167-1-1
Abstract
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.
