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reasonings in the world could never lead us one step towards the knowledge of it [18, p. 327]. With his skeptical analysis of philosophical reason, Hume had set a standard of reflection that forbade any further uncritical use of metaphysical ideas—even the apparently clear and fundamental concept of causality. But a rigorous application of his skeptical… (More)

- Britta Dorn, Eberhard Karls, Rainer Nagel, Abdelaziz Rhandi
- 2005

Hiermit erkläre ich, dass ich die Arbeit selbständig und nur mit den angegebenen Hilfsmitteln angefertigt habe und dass alle Stellen, die dem Wortlaut oder dem Sinne nach anderen Werken entnommen sind, durch Angabe der Quellen als Entlehnung kenntlich gemacht worden sind.

In this paper we survey results concerning the asymptotic properties of C0-semigroups on Banach spaces with respect to the weak operator topology. The property “no eigenvalues of the generator on the imaginary axis” is equivalent to weak stability for most time values; a phenomenon called ‘almost weak stability’. Further, sufficient conditions actually… (More)

In this paper, we present two quite general approximation theorems for the propagators of higher order (in time) abstract Cauchy problems, which extend largely the classical Trotter-Kato type approximation theorems for strongly continuous operator semigroups and cosine operator functions. Then, we apply the approximation theorems to deal with the second… (More)

- Rainer Nagel
- 1997

We propose an abstract framework for the computation of the spectrum (A) of a linear operator A : D(A) X ! X on a Banach space X through a condition in a smaller Banach space X 1. If this space is nite dimensional this yields a characteristic equation for (A). The method is tested for delay, integro-diierential and population equations and is applicable to… (More)

- SIMON BRENDLE, Rainer Nagel
- 2002

We consider a strongly continuous semigroup (T (t))t≥0 with generator A on a Banach space X, an A-bounded perturbation B, and the semigroup (S(t))t≥0 generated by A + B. Using the critical spectrum introduced recently, we improve existing spectral mapping theorems for the perturbed semigroup (S(t))t≥0. The results are applied to a cell equation with age… (More)

- David Cramer, Rainer Nagel
- 2002

We give a brief survey of applications of the Gearhart-Prüss spectral mapping theorem for abstract strongly continuous semigroups on Hilbert spaces to the study of stability of solitary waves for a large class of Hamiltonian partial differential equations of mathematical physics including Klein-Gordon, nonlinear Schrödinger, Boussinesq, Benjamin-BonaMahoney… (More)

- Rainer Nagel
- 1998

For a strongly continuous semigroup (T (t))t≥0 with generator A we introduce its critical spectrum σcrit(T (t)). This yields in an optimal way the spectral mapping theorem σ(T (t)) = e ∪ σcrit(T (t)) and improves classical stability results.

For a generator A of a C0 -semigroup T (·) on a Banach space X we consider the semi-norm Mk x := lim supt→0+ ‖t−1(T (t)− I)Ak−1x‖ on the Favard space Fk of order k associated with A . The use of this semi-norm is motivated by the functional analytic treatment of time-discretization methods of linear evolution equations. We show that sharp inequalities for… (More)