## Taiwanese Journal of Mathematics

### N-TIMES INTEGRATED C-SEMIGROUPS AND THE ABSTRACT CAUCHY PROBLEM

#### Abstract

This paper is concerned with generation theorems for exponentially equicontinuous $n$-times integrated $C$-semigroups of linear operators on a sequentially complete locally convex space (SCLCS). The generator of a nondegenerate $n$-times integrated $C$-semigroup is characterized. The proofs will base on a SCLCS-version of the Widder-Arendt theorem about the Laplace transforms of Lipschitz continuous functions, and on some properties of a $C$-pseudoresolvent. We also discuss the existence and uniqueness of solutions of the abstract Cauchy problem: $u'=Au+f,~u(0)=x$, for $x\in C(D(A^{n+1}))$ and suitable function $f$.

#### Article information

Source
Taiwanese J. Math., Volume 1, Number 1 (1997), 75-102.

Dates
First available in Project Euclid: 18 July 2017

https://projecteuclid.org/euclid.twjm/1500404927

Digital Object Identifier
doi:10.11650/twjm/1500404927

Mathematical Reviews number (MathSciNet)
MR1435499

Zentralblatt MATH identifier
0892.47042

#### Citation

Li, Y.-C.; Shaw, S.-Y. N-TIMES INTEGRATED C-SEMIGROUPS AND THE ABSTRACT CAUCHY PROBLEM. Taiwanese J. Math. 1 (1997), no. 1, 75--102. doi:10.11650/twjm/1500404927. https://projecteuclid.org/euclid.twjm/1500404927