On local α-times integrated C-semigroups

This paper presents several characterizations of a local alpha- times integrated C- semigroup {T( t); 0 <= t < tau} by means of functional equation, subgenerator, and well- posedness of an associated abstract Cauchy problem. We also discuss properties concerning the nondegeneracy of T( center dot), the injectivity of C, the closability of subgenerators, the commutativity of T( center dot), and extension of solutions of the associated abstract Cauchy problem. Copyright (c) 2007 Y.- C. Li and S.- Y. Shaw.