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An analyticity criterion for regularized semigroups


Authors: Quan Zheng and Yongsheng Zhao
Journal: Proc. Amer. Math. Soc. 130 (2002), 2271-2274
MSC (2000): Primary 47D62
DOI: https://doi.org/10.1090/S0002-9939-02-06219-6
Published electronically: March 15, 2002
MathSciNet review: 1896408
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Abstract: A generalization of Kato's analyticity criterion for $C_0$-semigroups to exponentially bounded regularized semigroups is given by using the method of Laplace transforms.

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

  • 1. R. deLaubenfels, Existence Families, Functional Calculi and Evolution Equations, Lect. Notes in Math., Vol. 1570, Springer-Verlag, Berlin, 1994. MR 96b:47047
  • 2. S. Kantorovitz, On Liu's analyticity criterion for semigroups, Semigroup Forum 53 (1996), 262-265. MR 97d:47042
  • 3. T. Kato, Perturbation Theory for Linear Operators, 2nd. ed., Springer-Verlag, Berlin, 1976. MR 53:11389
  • 4. Y. Liu, An equivalent condition for analytic $C_0$-semigroups, J. Math. Anal. Appl. 180 (1993), 71-78. MR 94i:47062
  • 5. F. Neubrander, Abstract elliptic operators, analytic interpolation semigroups and Laplace transforms of analytic functions, Semesterbericht Funktionalanalysis, Tübingen, Wintersemester 15 (1988/89), 163-185.
  • 6. Q. Zheng, Controllability of a class of linear systems in Banach spaces, Proc. Amer. Math. Soc. 123 (1995), 1241-1251. MR 95e:93011
  • 7. Q. Zheng and Y. Lei, Exponentially bounded $C$-semigroups and integrated semigroups with nondensely defined generators III: Analyticity, Acta Math. Scientia 14 (1994), 107-119. MR 95m:47065

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Additional Information

Quan Zheng
Affiliation: Department of Mathematics, Huazhong University of Science and Technology, Wuhan 430074, People’s Republic of China

Yongsheng Zhao
Affiliation: Department of Mathematics, Huazhong University of Science and Technology, Wuhan 430074, People’s Republic of China

DOI: https://doi.org/10.1090/S0002-9939-02-06219-6
Keywords: Regularized semigroup, analyticity, abstract Laplace transform
Received by editor(s): December 14, 1999
Received by editor(s) in revised form: November 1, 2000
Published electronically: March 15, 2002
Additional Notes: This project was supported by the National Science Foundation of China and the Foundation for Excellent Young Teachers of China
Communicated by: Joseph A. Ball
Article copyright: © Copyright 2002 American Mathematical Society

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