Rainer Nagel

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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)
In this article we survey results concerning 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 implying(More)
We consider a strongly continuous semigroup (T(t)) t0 with generator A on a Banach space X, an Abounded perturbation B, and the semigroup (S(t)) t0 generated by A + B. Using the critical spectrum introduced recently, we improve existing spectral mapping theorems for the perturbed semigroup (S(t)) t0. The results are applied to a cell equation with age(More)