Inhaltsverzeichnis - Mathematisches Institut der Universität zu Köln

DMV Tagung 2011 - Köln, 19. - 22. September
Sebastian Häsler
Technische Universität Chemnitz
Generalized solutions and spectrum for Dirichlet forms on graphs
We study the connection of the existence of solutions with certain properties and the spectrum of
operators in the framework of regular Dirichlet forms on infinite graphs. In particular we prove a version of
the Allegretto-Piepenbrink theorem, which says that positive (super-)solutions to a generalized eigenvalue
equation exist exactly for energies not exceeding the infimum of the spectrum. Moreover we show a
version of Shnol’s theorem, which says that existence of solutions satisfying a growth condition with
respect to a given boundary measure implies that the corresponding energy is in the spectrum.
Joshua Isralowitz
Universität zu Göttingen
Schatten class Toeplitz and Hankel operators on the Segal-Bargmann and Bergman spaces
We discuss and compare Schatten p class membership for 0 < p < ∞ of Toeplitz and Hankel operators
on the Segal-Bargmann space and the Bergman space of the unit ball in C n . In particular, we discuss
the cut-off phenomenon that occurs when characterizing Schatten p class membership of Toeplitz and
Hankel operators on the Bergman space of the unit ball, but which does not occur when characterizing
Schatten class Toeplitz and Hankel operators on the Segal-Bargmann space. This is partly joint work with
K. Zhu.
Birgit Jacob
Bergische Universität Wuppertal
Weighted interpolation in Paley-Wiener spaces and finite-time controllability
We consider the solution of weighted interpolation problems in model subspaces of the Hardy space
H 2 that are canonically isometric to Paley–Wiener spaces of analytic functions. A new necessary and
sufficient condition is given on the set of interpolation points which guarantees that a solution in H2 can
be transferred to a solution in a model space. The techniques used rely on the reproducing kernel thesis
for Hankel operators, which is given here with an explicit constant. One of the applications of this work is
to the finite-time controllability of diagonal systems specified by a C0 semigroup.
Literatur
B. Jacob, J.R. Partington and S. Pott. Weighted interpolation in Paley-Wiener spaces and finite-time controllability,
Journal of Functional Analysis, 259 (2010), 2424-2436
187