On the spectrum determined growth assumption and the perturbation of C 0 semigroups

Integral Equations and Operator Theory

Volumn 39, Issue 3, 2001, Pages 363-376

  Xu, Gen Qi ^a   Feng, De Xing ^a  

^a INSTITUTE OF SYSTEMS SCIENCE   (China)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0039250215     PISSN: 0378620X     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF01332662     Document Type: Article

References (29)

1. Gearhart, I., Spectral theory for contraction semigroup on Hilbert space, Trans. Amer. Math. Soc., 236(1978), 385-394.
2. Herbst, I. W., The spectrum of Hilbert space semigroups, J. Oper. Theory, 10(1983), 87-94.
3. 0 semigroups, Trans. Amer. Math. Soc., 284(1984), 847-857.
4. Nagel, R., One-parameter semigroups of positive operator, LNM 1184, Springer (1986). pp. 60-96.
5. Datko, R., Uniform asymptotic stability of evolutionary process in Banach space, SIAM J. Math. Anal., 3(1972), 428-445.
6. 0 semigroups, Chinese Science Bulletin, 39(1994), 534-537.
7. Prüss, J., Equilibrium solutions of age-specific population dynamics of several species, J. Math. Biology, 11(1981), 65-84.
8. Webb, G. F., Theory of Nonlinear Age-Dependent Population Dynamics, Marcel Dekker, INC, New York, Basel, 1985.
9. 0 semigroups, Bulletin de L' Académie Polonaise des Sciences, Math., Astro, et. Phys., 23(1975), 8, 885-895.
10. Greiner, G., J. Voiget and M. P. H. Wolff, On the spectral bound of the generator of semigroups of positive operators, J. Oper. Theory, 5(1981), 245-256.
11. 0 semigroups, Math. Ann., 285(1989), 201-219.
12. Pazy, A., Semigroups of Linear Operators and Applications to Partial Differential Equations, Springer-Verlag, New York, 1983.
13. 0 semigroup, Acta Math. Sinica., 33(1990), 6, 757-763.
14. Huang, F. L., Characteristic conditions for exponential stability of linear dynamical systems in Hilbert space, Ann. Diff. Eqs., 1(1985), 43-56.
15. Huang, F. L., Exponential stability of linear systems in Banach space, Chin. Ann. Math., 10 B(1989), 3, 332-340.
16. 0 semigroups, J. Math. Anal & Appl., 217(1998), 624-636.
17. Young, R. M., An introduction to Nonharmonic Fourier Series, Academic Press, 1980, pp. 80-150.
18. Kwapien, S., Isomorphic characterization of inner product space by orthogonal series with vector-valued coefficients, Studia Math., 44(1972), 583-595.
19. John, B. C., Functions of One Complex Variable, Springer-Verlag, New York, Berlin, 1978, pp. 153-159.
20. Bauer, F. L. and C. T. Fike, Norms and theorems, Numer. Math, 1960, 2, 137-141.
21. Kato, T., Perturbation Theory for Linear Operators, Springer-Verlag, New York, Berlin, 1984, pp. 28-29.
22. 0 semigroups, Communication in Partial Differential Equations, 18(1993), 7&8, 1299-1307.
23. Kim, J. U., Exponential decay of the energy of a one-dimensional inhomogeneous medium, SIAM J. Control & Optim., 29(1991), 368-380.
24. Munoz Rivera, J. A., Energy decay rates in linear thermoelasticity, Funk. Ekv., 35(1992), 19-30
25. Feng, D. X. and G. T. Zhu, Spectral properties of principal operators for a class of elastic vibration problems, Chinese Science Bulletin, Special issue, 1983, 79-82.
26. Hansen, S. W., Frequency Proportional Damping Models for the Euler-Bernoulli Beam Equation, Thesis, University of Wisconsin-Madison, December, 1988.
27. Shi, D. H., H. S. Hou and D. X. Feng, Feedback stabilization of a Timoshenko beam with an end mass, International Journal of Control, 69(1998), 2, 285-300.
28. Xu, C. Z., G. Weiss and B. Z. Guo, Exact observability, Riesz basis and spectrum determined growth condition, to appear.
29. Guo, B. Z., The Riesz basis property of discrete operators and applications to a linear thermoelastic system, to appear in IMA Journal of Math. Control and Information.