The spectral mapping theorem for evolution semigroups on spaces of vector-valued functions

1. Arendt, W.,Gaussian estimates and interpolation of the spectrum in L ^p, Differ. Integral Equ.7 (1994), 1153–1168.

   MATH  MathSciNet  Google Scholar 

2. Calderon, A. P.,Spaces between L ¹ and L ^∞ and the theorem of Marcinkiewicz, Studia Math.26 (1966), 273–299.

   MATH  MathSciNet  Google Scholar 

3. Coppel, W.A., “Dichotomies in Stability Theory,” Springer-Verlag, Berlin, 1978.

   MATH  Google Scholar 

4. Daleckij, Ju. L., and M. G. Krein, “Stability of Solutions of Differential Equations in Banach Spaces,” Transl. Math. Monogr., Vol. 4, Amer. Math. Soc., Providence R.I., 1974.

   Google Scholar 

5. Evans, D. E.,Time dependent perturbations and scattering of strongly continuous groups on Banach spaces, Math. Ann.221 (1976), 275–290.

   Article  MATH  MathSciNet  Google Scholar 

6. Fattorini, H. O., “The Cauchy Problem,” Addison-Wesley, Reading, 1983.

   Google Scholar 

7. Howland, J. S.,Stationary scattering theory for time-dependent Hamiltonians, Math. Ann.207 (1974), 315–335.

   Article  MATH  MathSciNet  Google Scholar 

8. Latushkin, Y., and S. Montgomery-Smith,Evolutionary semigroups and Lyapunov theorems in Banach spaces, J. Funct. Anal. (to appear).

9. Latushkin, Y., and S. Montgomery-Smith,Lyapunov theorems for Banach spaces, Bull. Am. Math. Soc.31 (1994), 44–49.

   Article  MATH  MathSciNet  Google Scholar 

10. Latushkin, Y., and T. W. Randolph,Dichotomy of differential equations on Banach spaces and an algebra of weighted translation operators, preprint.

11. Lindenstrauss, J., and L. Tzafiri, “Classical Banach Spaces II, Function Spaces,” Springer-Verlag, Berlin, 1979.

    MATH  Google Scholar 

12. Lumer, G.,Equations de diffusion dans le domaine (x,t) non-cylindriques et semigroupes “éspace-temps”, in: “Séminaire de Théorie du Potentiel Paris,” No. 9, Springer-Verlag, 1989, 161–179.

13. Nagel, R. (Ed.), “One-Parameter Semigroups of Positive Operators,” Springer-Verlag, Berlin, 1984.

    Google Scholar 

14. Nagel, R.,Semigroup methods for non-autonomous Cauchy problems, Tübinger Berichte zur Funktionalanalysis2, Tübingen, 1993.

15. Nagel, R., and E. Sinestrari,Inhomogeneous Volterra integrodifferential equations for Hille-Yosida operators, in: “Functional Analysis,” K. D. Bierstedt, A. Pietsch, W. M. Ruess, D. Vogt (Eds.), Proc. Essen Conference, 1993, 51–72.

16. Neidhardt, H.,On abstract linear evolution equations I, Math. Nachr.103 (1981), 283–293.

    MATH  MathSciNet  Google Scholar 

17. Paquet, L.,Semigroupes géneralisés et équations d'évolution, in: “Séminaire de Théorie du Potentiel Paris,” No. 4, Springer-Verlag, 1979, 243–263.

18. Pazy, A., “Semigroups of Linear Operators and Applications to Partial Differential Equations,” Springer-Verlag, Berlin, 1983.

    MATH  Google Scholar 

19. Räbiger, F., and R. Schnaubelt,A spectral characterization of exponentially dichotomic and hyperbolic evolution families, Tübinger Berichte zur Funktionalanalysis3, Tübingen, 1994.

20. Räbiger, F., Rhandi, A., and R. Schnaubelt,Perturbation and an abstract characterization of evolution semigroups, Tübiger Berichte zur Funktionalanalysis3, Tübingen, 1994.

21. Rau, R., Hyperbolic evolution semigroups, Dissertation, Tübingen, 1992.

22. Rau, R.,Hyperbolic evolution groups and dichotomic evolution families, J. Dyn. Differ. Equations6 (1994), 335–350.

    Article  MATH  MathSciNet  Google Scholar 

23. Rau, R.,Hyperbolic evolution semigroups on vector valued function spaces, Semigroup Forum48 (1994), 107–118.

    MATH  MathSciNet  Google Scholar 

24. Rhandi, A., Lipschitz stetige Evolutionsfamilien und die exponentielle Dichotomie, Dissertation, Tübingen, 1994.

25. Schaefer, H. H., “Banach Lattices and Positive Operators,” Springer-Verlag, Berlin, 1974.

    MATH  Google Scholar 

26. Sacker, R. J., and G. R. Sell,Dichotomies for linear evolutionary equations in Banach spaces, IMA preprint No. 838 (1991).

27. Tanabe, H., “Equations of Evolution,” Pitman, London, 1979.

    MATH  Google Scholar 

28. Triebel, H., “Interpolation Theory, Function Spaces, Differential Operators,” North-Holland, Amsterdam, New York, Oxford, 1978.

    Google Scholar 

Download references