Buchbeiträge:
H. Woracek:
"Existance of zerofree functions $N$-associated to a de Branges Pontryagin space";
in: "ASC Report 23/2009",
herausgegeben von: Institute for Analysis and Scientific Computing;
Vienna University of Technology,
Wien,
2009,
ISBN: 978-3-902627-02-5.
Kurzfassung englisch:
In the theory of de Branges Hilbert spaces of entire functions, so-called
`functions associated to a space´ play an important role. In the present
paper we deal with a generalization of this notion in two directions, namely
with functions N-associated (N 2 Z) to a de Branges Pontryagin space.
Let a de Branges Pontryagin space P and N 2 Z be given. Our aim
is to characterize whether there exists a real and zerofree function Nassociated
to P in terms of Kre˘ın´s Q-function associated with the multiplication
operator in P. The conditions which appear in this characterization
involve the asymptotic distribution of the poles of the Q-function
plus a summability condition.
Although this question may seem rather abstract, its answer has a variety
of nontrivial consequences. We use it to answer two questions arising
in the theory of general (indefinite) canonical systems. Namely, to characterize
whether a given generalized Nevanlinna function is the intermediate
Weyl-coefficient of some system in terms of its poles and residues, and to
characterize whether a given general Hamiltonian ends with a specified
number of indivisible intervals in terms of the Weyl-coefficient associated
to the system. In addition, we present some applications, e.g. dealing with
admissible majorants in de Branges spaces or the continuation problem
for hermitian indefinite functions.
Schlagworte:
de Branges space, Pontryagin space, associated function, canonical
"Offizielle" elektronische Version der Publikation (entsprechend ihrem Digital Object Identifier - DOI)
http://dx.doi.org/10.1007/s00605-010-0203-2
Elektronische Version der Publikation:
http://www.asc.tuwien.ac.at/preprint/2009/asc23x2009.pdf
Erstellt aus der Publikationsdatenbank der Technischen Universität Wien.