LOCAL C-SEMIGROUPS AND LOCAL C-COSINE FUNCTIONS

This paper is concerned with the local C-semigroups and local C-cosine functions without the assumption that the image of C is dense in a Banach space X, First, the sufficient and necessary conditions for a local C-semigroup and a C-cosine function to be the restriction of a global C-semigroup and a global C-cosine function to an interval are given, respectively, Secondly, it is characterized for a closed operator to be the generator of a local C-semigroup and a local C-cosine function, respectively.

The Reduction Square Root and Perturbation for a Class of Strongly Continuous Operator Families

We introduce the concept of a times C-second resolvent families and present the rela- tionship between a times C-resolvent families and a times C-second resolvent families. Moreover, the perturbation and square root for a times C-resolvent families are considered in this paper which generalize the counterparts of C-Cosine operator functions.

Abstract Volterra equations in locally convex spaces

A general class of(a,k)-regularized C-resolvent families is one of efficient research tools for dealing with non-degenerate abstract Volterra equations of scalar type.The main purpose of this expository paper is to provide a detailed analysis of the above class in sequentially complete locally convex spaces.