The critical spectrum of a strongly continuous semigroup

Advances in Mathematics

Volumn 152, Issue 1, 2000, Pages 120-133

  Nagel, Rainer ^a   Poland, Jan ^a  

^a UNIVERSITY OF TÜBINGEN   (Germany)

Author keywords

Generator; Growth bound; Spectral mapping theorem; Spectrum; Strongly continuous semigroup

Indexed keywords

EID: 0034196150     PISSN: 00018708     EISSN: None     Source Type: Journal    
DOI: 10.1006/aima.1998.1893     Document Type: Article

References (12)

1. Andreu F., Martínez J., Mazón J. M. A spectral mapping theorem for perturbed strongly continuous semigroups. Math. Ann. 291:1991;453-462.
2. M. D. Blake, A spectral bound for asymptotically norm-continuous semigroups, preprint, 1998.
3. Engel K., Nagel R. One-Parameter Semigroups for Linear Evolution Equations. Graduate Text in Math. 194:2000;Springer-Verlag, New York/Berlin.
4. Hille E., Phillips R. S. Functional Analysis and Semigroups. Amer. Math. Soc. Colloq. Publ. 31:1957;Amer. Math. Soc. Providence.
5. Kato T. Perturbation Theory for Linear Operators. 1966;Springer-Verlag, New York/Berlin.
6. Liapunov M. A. Problème Général de la Stabilité du Mouvement. 1949;Princeton Univ. Press, Princeton.
7. 0-semigroups norm continuous at infinity. Semigroup Forum. 52:1996;213-224.
8. Nagel R. One-Parameter Semigroups of Positive Operators. Lecture Notes in Math. 1184:1986;Springer-Verlag, New York/Berlin.
9. Renardy M. On the stability of differentiability of semigroups. Semigroup Forum. 51:1995;343-346.
10. Thieme H. R. Balanced exponential growth of operator semigroups. J. Math. Anal. Appl. 223:1998;30-49.
11. van Neerven J. The Asymptotic Behaviour of Semigroups of Linear Operators. Operator Theory Adv. Appl. 88:1996;Birkhäuser, Basel.
12. Voigt J. Stability of the essential type of strongly continuous semigroups. Trans. Steklov Math. Inst. 203:1994;469-477.