Rainer Nagel

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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)
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)
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)
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)