Korean Journal of Mathematics

The Kangwon-Kyungki Mathematical Society (강원경기수학회)
권호 표지

APPROXIMATION THEOREM FOR CONTRACTION C-SEMIGROUPS

  • Lee, Young S. (Department of Mathematics Seoul Women's University)
  • Received : 2010.06.23
  • Accepted : 2010.08.15
  • Published : 2010.09.30
Download PDF
⟨ Previous Next ⟩

Abstract

In this paper we establish approximation of contraction C-semigroups on the extrapolation space $X^C$, by showing the equicontinuity of contraction C-semigroups on $X^C$.

Keywords

References

  1. W. Arendt, C. J. K. Batty, M. Hieber and F. Neubrander, Vector-Valued Laplace Transforms and Cauchy Problems, Birkhaaser, 2001.
  2. R. deLaubenfels, Existence Families, Functional Calculi and Evolution Equations, Lecture Notes in Math. vol. 157, Springer-Verlag, 1994.
  3. K.J. Engel and R. Nagel, One Parameter Semigroups for Linear Evolution Equations, Springer-Verlag, 2000.
  4. M. Bachar, W. Desch and Mardiyana, A Class of Semigroups Regularized in Space and Time, J. Math. Anal. Appl. 314(2006), 558-578. https://doi.org/10.1016/j.jmaa.2005.04.032
  5. M. Li and F. L. Fuang, Characterization of Contraction C-semigroups, Proc. Amer. Math. Soc. 126(1998), 1063-1069. https://doi.org/10.1090/S0002-9939-98-04243-9
  6. Y. C. Li and S. Y. Shaw, N-times Integrated C-semigroups and the Abstract Cauchy Problems, Taiwanese J. Math. 1(1997), 75-102. https://doi.org/10.11650/twjm/1500404927
  7. T. J. Xiao and J. Liang, Approximations of Laplace Transforms and Integrated Semigroups, J. Funct. Anal. 172(2000), 202-220. https://doi.org/10.1006/jfan.1999.3545