References
Arendt, W.,Gaussian estimates and interpolation of the spectrum in L p, Differ. Integral Equ.7 (1994), 1153–1168.
Calderon, A. P.,Spaces between L 1 and L ∞ and the theorem of Marcinkiewicz, Studia Math.26 (1966), 273–299.
Coppel, W.A., “Dichotomies in Stability Theory,” Springer-Verlag, Berlin, 1978.
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.
Evans, D. E.,Time dependent perturbations and scattering of strongly continuous groups on Banach spaces, Math. Ann.221 (1976), 275–290.
Fattorini, H. O., “The Cauchy Problem,” Addison-Wesley, Reading, 1983.
Howland, J. S.,Stationary scattering theory for time-dependent Hamiltonians, Math. Ann.207 (1974), 315–335.
Latushkin, Y., and S. Montgomery-Smith,Evolutionary semigroups and Lyapunov theorems in Banach spaces, J. Funct. Anal. (to appear).
Latushkin, Y., and S. Montgomery-Smith,Lyapunov theorems for Banach spaces, Bull. Am. Math. Soc.31 (1994), 44–49.
Latushkin, Y., and T. W. Randolph,Dichotomy of differential equations on Banach spaces and an algebra of weighted translation operators, preprint.
Lindenstrauss, J., and L. Tzafiri, “Classical Banach Spaces II, Function Spaces,” Springer-Verlag, Berlin, 1979.
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.
Nagel, R. (Ed.), “One-Parameter Semigroups of Positive Operators,” Springer-Verlag, Berlin, 1984.
Nagel, R.,Semigroup methods for non-autonomous Cauchy problems, Tübinger Berichte zur Funktionalanalysis2, Tübingen, 1993.
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.
Neidhardt, H.,On abstract linear evolution equations I, Math. Nachr.103 (1981), 283–293.
Paquet, L.,Semigroupes géneralisés et équations d'évolution, in: “Séminaire de Théorie du Potentiel Paris,” No. 4, Springer-Verlag, 1979, 243–263.
Pazy, A., “Semigroups of Linear Operators and Applications to Partial Differential Equations,” Springer-Verlag, Berlin, 1983.
Räbiger, F., and R. Schnaubelt,A spectral characterization of exponentially dichotomic and hyperbolic evolution families, Tübinger Berichte zur Funktionalanalysis3, Tübingen, 1994.
Räbiger, F., Rhandi, A., and R. Schnaubelt,Perturbation and an abstract characterization of evolution semigroups, Tübiger Berichte zur Funktionalanalysis3, Tübingen, 1994.
Rau, R., Hyperbolic evolution semigroups, Dissertation, Tübingen, 1992.
Rau, R.,Hyperbolic evolution groups and dichotomic evolution families, J. Dyn. Differ. Equations6 (1994), 335–350.
Rau, R.,Hyperbolic evolution semigroups on vector valued function spaces, Semigroup Forum48 (1994), 107–118.
Rhandi, A., Lipschitz stetige Evolutionsfamilien und die exponentielle Dichotomie, Dissertation, Tübingen, 1994.
Schaefer, H. H., “Banach Lattices and Positive Operators,” Springer-Verlag, Berlin, 1974.
Sacker, R. J., and G. R. Sell,Dichotomies for linear evolutionary equations in Banach spaces, IMA preprint No. 838 (1991).
Tanabe, H., “Equations of Evolution,” Pitman, London, 1979.
Triebel, H., “Interpolation Theory, Function Spaces, Differential Operators,” North-Holland, Amsterdam, New York, Oxford, 1978.
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Communicated by Rainer Nagel
This paper is part of a research project supported by the Deutsche Forschungsgenschaft DFG.
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Räbiger, F., Schnaubelt, R. The spectral mapping theorem for evolution semigroups on spaces of vector-valued functions. Semigroup Forum 52, 225–239 (1996). https://doi.org/10.1007/BF02574098
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DOI: https://doi.org/10.1007/BF02574098