Local K-Convoluted C-groups and Abstract Cauchy Problem

Abstract

We first present a new form of a local K-convoluted C-group on a Banach space X, and then deduce some basic properties of a nondegenerate local K-convoluted C-group on X and some generation theorems of local K-convoluted C-groups, which can be applied to obtain some equivalence relations between the generation of a nondegenerate local K-convoluted C-group on X with subgenerator A and the unique existence of solutions of the abstract Cauchy problem ACP(A,f,x).