The Approximation Theorems And Spectral Mapping Theorems For N-times Integrated C-semigroups

The spectral mapping theorem and the approximation theorem for semigroups is an important aspect of semigroups thoery. In this paper we will extend these thoeries on n-times Integreted C-semigroups. In the chapter two of this paper, we will abttain several thoeries by Laplace transforms and the approximation of a sequence of generators. In the chapter three,we will get several spectral mapping theorems by discussing the relationship between the spectral of n-times Integrated C-semigroups and the spectral of its generator. These thoeries will extend the applied range of the approximation theorem and the spectral mapping theorem.