Local integrated $C$-semigroups
Volume 145 / 2001
Studia Mathematica 145 (2001), 265-280
MSC: 47D62, 47D60, 47D06, 47D03.
DOI: 10.4064/sm145-3-6
Abstract
We introduce the notion of a local $n$-times integrated $C$-semigroup, which unifies the classes of local $C$-semigroups, local integrated semigroups and local $C$-cosine functions. We then study its relations to the $C$-wellposedness of the $(n+1)$-times integrated Cauchy problem and second order abstract Cauchy problem. Finally, a generation theorem for local $n$-times integrated $C$-semigroups is given.
