Some Conclusions about alpha-times Integrated C Semigroups

Abstract

This paper gets two main conclusions about ®-times integrated C semi groups based on the Hille exponential formulas of the other kinds of semi groups, the generation theorem in terms of the Laplace transform and the properties of exponential bounded ®-times integrated C semi groups. One is the representation theorem, the other is the Laplace inverse transform as well as two deductions.