数学物理学报(英文版) ›› 1993, Vol. 13 ›› Issue (3): 251-260.

• 论文 • 上一篇    下一篇

EXPONENTIALLY BOUNDED C-SEMIGROUP AND INTEGRATED SEMIGROUP WITH NONDENSELY DEFINED GENERATORS I:APPROXIMATION

郑权1, 雷岩松2   

  1. 1. Dept. of Math., Huazhong Univ. of Sci. & Tech., Wuhan 430074, China;
    2. Dept. of Math., China Univ. of Geosci., Wuhan 430074, China
  • 收稿日期:1991-03-27 出版日期:1993-09-25 发布日期:1993-09-25
  • 基金资助:
    This project is supported by the National Science Foundation of China.

EXPONENTIALLY BOUNDED C-SEMIGROUP AND INTEGRATED SEMIGROUP WITH NONDENSELY DEFINED GENERATORS I:APPROXIMATION

Zheng Quan1, Lei Yansong2   

  1. 1. Dept. of Math., Huazhong Univ. of Sci. & Tech., Wuhan 430074, China;
    2. Dept. of Math., China Univ. of Geosci., Wuhan 430074, China
  • Received:1991-03-27 Online:1993-09-25 Published:1993-09-25
  • Supported by:
    This project is supported by the National Science Foundation of China.

摘要: In this paper, by Laplace transform version of the Trotter-Kato approximation theorem and the integrated C-semigroup introduced by Myadera, the authors obtained some Trotter-Kato approximation theorems on exponentially bounded C-semigroups, where the range of C (and so the domain of the generator) may not be dense. The authors deduced the corresponding results on exponentially bounded integrated semigroups with nondensely generators. The results of this paper extended and perfected the results given by Lizama, Park and Zheng.

Abstract: In this paper, by Laplace transform version of the Trotter-Kato approximation theorem and the integrated C-semigroup introduced by Myadera, the authors obtained some Trotter-Kato approximation theorems on exponentially bounded C-semigroups, where the range of C (and so the domain of the generator) may not be dense. The authors deduced the corresponding results on exponentially bounded integrated semigroups with nondensely generators. The results of this paper extended and perfected the results given by Lizama, Park and Zheng.