Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Generation theorems for $\varphi $ Hille-Yosida operators


Author: Sheng Wang Wang
Journal: Proc. Amer. Math. Soc. 130 (2002), 3355-3367
MSC (2000): Primary 47D05; Secondary 47B40
DOI: https://doi.org/10.1090/S0002-9939-02-06606-6
Published electronically: May 29, 2002
MathSciNet review: 1913015
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: This paper introduces the concept of $\varphi $ Hille-Yosida operators and studies several generation theorems. We show that if a once-integrated semigroup $\{S(t) \}_{t \geq 0}$ satisfies $\Phi (t) := limsup_{h \rightarrow 0^{+}} \frac{1}{h} \vert\vert S(t + h) - S(t)\vert\vert < \infty $ for all $t > 0 a. e.$, then $\Phi (\cdot )$ is locally bounded on $(0, \infty )$ and exponentially bounded. In addition, some other interesting results are presented.


References [Enhancements On Off] (What's this?)

  • 1. W. Arendt, Vector-valued Laplace transforms and Cauchy problems, Israel J. Math., V. 59 (1987), 327-353. MR 89a:47064
  • 2. W. Arendt et. al, Resolvent Positive Operators, Proc. London Math., V. 54 (1987), 321-349. MR 88c:47074
  • 3. Ph. Clement et. al, A Hille-Yosida theorem for a class of weak* continuous semigroups, Semigroup Forum, V. 38 (1989), 157-178. MR 90c:47066
  • 4. R. deLaubenfels, Existence Families, Functional Calculi and Evolution Equations, Lect. Notes in Math., Springer-Verlag, V. 1570, 1994. MR 96b:47047
  • 5. R. deLaubenfels, Q. P. Vu and S. W. Wang, Laplace transforms of vector-valued functions with growth $\omega $ and semigroups of operators, Semiproup Furom, to appear.
  • 6. E. Hille and R. S. Phillips, Functional Analysis and Semigroups, Amer. Math. Soc. Colloq. Pub., Vol. V. 31, Providence, R. I., 1957. MR 19:664d; reprinting of revised edit. MR 54:11077
  • 7. H. Kellerman and M. Hieber, Integrated Semigroups, J. Funct. Anal., V. 84 (1989), 160-180. MR 90h:47072
  • 8. I. Miyadera, On one-parameter semi-groups of operators, J. Math. Tokyo, V. 1 (1951), 23-26. MR 14:564d
  • 9. J. van Neerven, The Adjoint of a Semigroup of Linear Operators, Lect. Notes in Math., Springer-Verlag, V. 1529, 1992. MR 94j:47059
  • 10. H. R. Thieme, Integrated semigroups and integrated solutions to abstract Cauchy problems, J. Math. Anal. Appl., V. 152 (1990), 416-447. MR 91k:47093
  • 11. S. W. Wang, Mild integrated C-existence families, Studia Math., V. 112 (1995), 251-266. MR 95m:47067
  • 12. S. W. Wang, Quasi-distribution semigroups and integrated semigroups, J. Funct. Anal., V. 146 (1997), 352-381. MR 98d:47088
  • 13. S. W. Wang and I. Erdelyi, Abel-Ergodic properties of Pseudo-resolvents and Applications to Semigroups, Tôkohu Math. J., V. 45 (1993), 539-554. MR 95g:47011
  • 14. D. V. Widder, An Introduction to Transform Theory, Acad. Press, New York, 1971.

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 47D05, 47B40

Retrieve articles in all journals with MSC (2000): 47D05, 47B40


Additional Information

Sheng Wang Wang
Affiliation: Department of Mathematics, Nanjing University, Jiangsu 210093, People’s Republic of China
Email: wang2598@netra.nju.edu.cn

DOI: https://doi.org/10.1090/S0002-9939-02-06606-6
Received by editor(s): June 7, 2000
Received by editor(s) in revised form: June 26, 2001
Published electronically: May 29, 2002
Communicated by: David R. Larson
Article copyright: © Copyright 2002 American Mathematical Society

American Mathematical Society