PL EN


Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
Czasopismo
1999 | 132 | 2 | 141-149
Tytuł artykułu

On the exponential stability and dichotomy of $C_0$-semigroups

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
A characterization of exponentially dichotomic and exponentially stable $C_0$-semigroups in terms of solutions of an operator equation of Lyapunov type is presented. As a corollary a new and shorter proof of van Neerven's recent characterization of exponential stability in terms of boundedness of convolutions of a semigroup with almost periodic functions is given.
Słowa kluczowe
Czasopismo
Rocznik
Tom
132
Numer
2
Strony
141-149
Opis fizyczny
Daty
wydano
1999
otrzymano
1997-12-15
poprawiono
1998-06-01
Twórcy
Bibliografia
  • [1] W. Arendt, F. Räbiger and A. Sourour, Spectral properties of the operator equation AX+XB=Y, Quart. J. Math. Oxford Ser. (2) 45 (1994), 133-149.
  • [2] Ju. L. Daleckiĭ [Yu. L. Daletskiĭ] and M. G. Krein, Stability of Solutions of Differential Equations on Banach Spaces, Amer. Math. Soc., Providence, R.I., 1974.
  • [3] R. Datko, Extending a theorem of A. M. Liapunov to Hilbert space, J. Math. Anal. Appl. 32 (1970), 610-616.
  • [4] I. Erdelyi and S. W. Wang, A Local Spectral Theory for Closed Operators, London Math. Soc. Lecture Note Ser. 105, Cambridge Univ. Press, Cambridge, 1985.
  • [5] J. M. Freeman, The tensor product of semigroups and the operator equation SX-XT=A, J. Math. Mech. 19 (1970), 819-828.
  • [6] J. Goldstein, On the operator equation AX+XB=Q, Proc. Amer. Math. Soc. 78 (1978), 31-34.
  • [7] Yu. Latushkin and S. Montgomery-Smith, Evolutionary semigroups and Lyapunov theorems in Banach spaces, J. Funct. Anal. 127 (1995), 173-197.
  • [8] S. C. Lin and S. Y. Shaw, On the operator equations Ax=q and SX-XT=Q, ibid. 77 (1988), 352-363.
  • [9] G. Lumer and M. Rosenblum, Linear operator equations, Proc. Amer. Math. Soc. 10 (1959), 32-41.
  • [10] R. Nagel (ed.), One-Parameter Semigroups of Positive Operators, Lecture Notes in Math. 1184, Springer, Berlin, 1986.
  • [11] J. M. A. M. van Neerven, The Asymptotic Behavior of a Semigroup of Linear Operators, Birkhäuser, Basel, 1996.
  • [12] A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations, Springer, New York, 1983.
  • [13] J. Prüss, On the spectrum of $C_0$-semigroups, Trans. Amer. Math. Soc. 284 (1984), 847-857.
  • [14] C. R. Putnam, Commutation Properties of Hilbert Space Operators and Related Topics, Springer, New York, 1967.
  • [15] M. Rosenblum, On the operator equation BX-XA=Q, Duke Math. J. 23 (1956), 263-269.
  • [16] Vũ Quôc Phóng, The operator equation AX-XB=C with unbounded operators A and B and related abstract Cauchy problems, Math. Z. 208 (1991), 567-588.
  • [17] Vũ Quôc Phóng, On the spectrum, complete trajectories, and asymptotic stability of linear semidynamical systems, J. Differential Equations 105 (1993), 30-45.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-smv132i2p141bwm
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.