On the spectral bound of the generator of a C 0 -semigroup

Yu. Tomilov

Studia Mathematica (1997)

  • Volume: 125, Issue: 1, page 23-33
  • ISSN: 0039-3223

Abstract

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We give several conditions implying that the spectral bound of the generator of a C 0 -semigroup is negative. Applications to stability theory are considered.

How to cite

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Tomilov, Yu.. "On the spectral bound of the generator of a $C_0$-semigroup." Studia Mathematica 125.1 (1997): 23-33. <http://eudml.org/doc/216419>.

@article{Tomilov1997,
abstract = {We give several conditions implying that the spectral bound of the generator of a $C_0$-semigroup is negative. Applications to stability theory are considered.},
author = {Tomilov, Yu.},
journal = {Studia Mathematica},
keywords = {spectral bound of the generator; -semigroup is negative; stability theory},
language = {eng},
number = {1},
pages = {23-33},
title = {On the spectral bound of the generator of a $C_0$-semigroup},
url = {http://eudml.org/doc/216419},
volume = {125},
year = {1997},
}

TY - JOUR
AU - Tomilov, Yu.
TI - On the spectral bound of the generator of a $C_0$-semigroup
JO - Studia Mathematica
PY - 1997
VL - 125
IS - 1
SP - 23
EP - 33
AB - We give several conditions implying that the spectral bound of the generator of a $C_0$-semigroup is negative. Applications to stability theory are considered.
LA - eng
KW - spectral bound of the generator; -semigroup is negative; stability theory
UR - http://eudml.org/doc/216419
ER -

References

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  1. [1] C. J. K. Batty, Tauberian theorems for the Laplace-Stieltjes transform, Trans. Amer. Math. Soc. 322 (1990), 783-804. Zbl0716.44001
  2. [2] C. J. K. Batty, Asymptotic behaviour of semigroups of operators, in: Functional Analysis and Operator Theory, J. Zemánek (ed.), Banach Center Publ. 30, Inst. Math., Polish Acad. Sci., Warszawa, 1994, 35-52. Zbl0818.47034
  3. [3] P. Clément et al., One-Parameter Semigroups, CWI Monograph 5, North-Holland, 1987. 
  4. [4] E. B. Davies, One-Parameter Semigroups, Academic Press, London, 1980. Zbl0457.47030
  5. [5] E. Hille and R. S. Phillips, Functional Analysis and Semi-Groups, Colloq. Publ. 31, Amer. Math. Soc., Providence, R.I., 1957. Zbl0078.10004
  6. [6] K. Hoffman, Banach Spaces of Analytic Functions, Prentice-Hall, Englewood Cliffs, N.J., 1962. Zbl0117.34001
  7. [7] A. Lebow, Spectral radius of an absolutely continuous operator, Proc. Amer. Math. Soc. 36 (1972), 511-514. Zbl0273.47001
  8. [8] G. Mil'shteĭn, Extension of semigroups to locally convex spaces, Izv. Vuz. Mat. 2 (1977), 91-95 (in Russian). 
  9. [9] W. Mlak, On a theorem of Lebow, Ann. Polon. Math. 35 (1977), 107-109. Zbl0371.47007
  10. [10] J. van Neerven, The Asymptotic Behavior of Semigroups of Linear Operators, Oper. Theory Adv. Appl. 88, Birkhäuser, Basel, 1996. 
  11. [11] N. K. Nikol'skiĭ, A Tauberian theorem on the spectral radius, Siberian Math. J. 18 (1977), 1367-1372. 
  12. [12] A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations, Appl. Math. Sci. 44, Springer, New York, 1983. Zbl0516.47023
  13. [13] M. Slemrod, Asymptotic behavior of C 0 -semigroups as determined by the spectrum of the generator, Indiana Univ. Math. J. 25 (1976), 783-792. Zbl0313.47026
  14. [14] G. Weiss, Weak L p -stability of a linear semigroup on a Hilbert space implies exponential stability, J. Differential Equations 76 (1988), 269-285. Zbl0675.47031
  15. [15] G. Weiss, Weakly l p -stable operators are power stable, Internat. J. Systems Sci. 20 (1989), 2323-2328. Zbl0686.93081
  16. [16] G. Weiss, The resolvent growth assumption for semigroups in Hilbert space, J. Math. Anal. Appl. 145 (1990), 154-171. Zbl0693.47034
  17. [17] V. Wrobel, Stability and spectra of C 0 -semigroups, Math. Ann. 285 (1989), 201-219. Zbl0698.47023
  18. [18] P. Yao and P. Feng, A characteristic condition for the exponential stability of C 0 -semigroups, Chinese Sci. Bull. 39 (1994), 534-537. Zbl0815.47056
  19. [19] J. Zabczyk, A note on C 0 -semigroups, Bull. Acad. Polon. Sci. Sér. Sci. Math. 23 (1975), 895-898. Zbl0312.47037

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