Vorträge

In the classical potential theory on the Euclidean space and in the potential theory of transient Markov chains a unique decomposition of superharmonic functions into a harmonic and a potential part is well-known. In this talk the basic concepts and ideas to gain such a decomposition for Schrödinger operators on graphs will be shown. The talk will show results of my master's thesis supervised by Matthias Keller.

Wie verändert sich das Spektrum des Laplace-Operators (oder allgemeiner von Schrödinger-Operatoren) auf metrischen Graphen unter Variation der Graphenparameter? Einige Antworten auf die Frage gibt es im Vortrag.

I will give a short summary of my master thesis as well as a quick introduction of myself.

Was wird aus (Pseudo-)Eigenwerten und -vektoren beim Abschneiden einer unendlichen Matrix? (Sie bleiben welche.)
Gibt es auch Aussagen in die umgekehrte Richtung?
Wie gut lassen sich diese Aussagen quantifizieren?

Vortrag (PDF, 1.0MB)

We construct extrapolation spaces for non-densely defined (weak) Hille--Yosida operators. In particular, we discuss extrapolation of bi-continuous semigroups. As an application we present a Desch--Schappacher type perturbation result for this kind of semigroups. This talk is based on joint work with B. Farkas.