Abstract and Applied Analysis
Volume 2007 (2007), Article ID 34890, 18 pages
On Local -Times Integrated -Semigroups
1Department of Applied Mathematics, National Chung-Hsing University, Taichung 402, Taiwan
2Graduate School of Engineering, Lunghwa University of Science and Technology, Taoyuan 333, Taiwan
Received 7 November 2006; Revised 22 April 2007; Accepted 20 July 2007
Academic Editor: Wolfgang Ruess
Copyright © 2007 Yuan-Chuan Li and Sen-Yen Shaw. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
This paper presents several characterizations of a local -times integrated -semigroup by means of functional equation, subgenerator, and well-posedness of an associated abstract Cauchy problem. We also discuss properties concerning the nondegeneracy of , the injectivity of , the closability of subgenerators, the commutativity of , and extension of solutions of the associated abstract Cauchy problem.