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1997 | 125 | 1 | 23-33
Tytuł artykułu

On the spectral bound of the generator of a $C_0$-semigroup

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
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.
Słowa kluczowe
Czasopismo
Rocznik
Tom
125
Numer
1
Strony
23-33
Opis fizyczny
Daty
wydano
1997
otrzymano
1995-11-10
poprawiono
1997-01-06
Twórcy
autor
Bibliografia
  • [1] C. J. K. Batty, Tauberian theorems for the Laplace-Stieltjes transform, Trans. Amer. Math. Soc. 322 (1990), 783-804.
  • [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.
  • [3] P. Clément et al., One-Parameter Semigroups, CWI Monograph 5, North-Holland, 1987.
  • [4] E. B. Davies, One-Parameter Semigroups, Academic Press, London, 1980.
  • [5] E. Hille and R. S. Phillips, Functional Analysis and Semi-Groups, Colloq. Publ. 31, Amer. Math. Soc., Providence, R.I., 1957.
  • [6] K. Hoffman, Banach Spaces of Analytic Functions, Prentice-Hall, Englewood Cliffs, N.J., 1962.
  • [7] A. Lebow, Spectral radius of an absolutely continuous operator, Proc. Amer. Math. Soc. 36 (1972), 511-514.
  • [8] G. Mil'shteĭn, Extension of semigroups to locally convex spaces, Izv. Vuz. Mat. 2 (1977), 91-95 (in Russian).
  • [9] W. Mlak, On a theorem of Lebow, Ann. Polon. Math. 35 (1977), 107-109.
  • [10] J. van Neerven, The Asymptotic Behavior of Semigroups of Linear Operators, Oper. Theory Adv. Appl. 88, Birkhäuser, Basel, 1996.
  • [11] N. K. Nikol'skiĭ, A Tauberian theorem on the spectral radius, Siberian Math. J. 18 (1977), 1367-1372.
  • [12] A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations, Appl. Math. Sci. 44, Springer, New York, 1983.
  • [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.
  • [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.
  • [15] G. Weiss, Weakly $l^p$-stable operators are power stable, Internat. J. Systems Sci. 20 (1989), 2323-2328.
  • [16] G. Weiss, The resolvent growth assumption for semigroups in Hilbert space, J. Math. Anal. Appl. 145 (1990), 154-171.
  • [17] V. Wrobel, Stability and spectra of $C_0$-semigroups, Math. Ann. 285 (1989), 201-219.
  • [18] P. Yao and P. Feng, A characteristic condition for the exponential stability of $C_0$-semigroups, Chinese Sci. Bull. 39 (1994), 534-537.
  • [19] J. Zabczyk, A note on $C_0$-semigroups, Bull. Acad. Polon. Sci. Sér. Sci. Math. 23 (1975), 895-898.
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Bibliografia
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bwmeta1.element.bwnjournal-article-smv125i1p23bwm
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