Contributions to Books:
M. Kaltenbäck, H. Woracek:
"Pontryagin spaces of entire functions VI";
in: "ASC Report 22/2009",
issued by: Institute for Analysis and Scientific Computing;
Vienna University of Technology,
In the theory of two-dimensional canonical (also called `Hamiltonian´)
systems, the notion of the Titchmarsh-Weyl coefficient associated to a
Hamiltonian function plays a vital role. A cornerstone in the spectral
theory of canonical systems is the Inverse Spectral Theorem due to Louis
de Branges which states that the Hamiltonian function of a given system
is (up to changes of scale) fully determined by its Titchmarsh-Weyl co-
efficient. Much (but not all) of this theory can be viewed and explained
using the theory of entire operators due to Mark G.Kre˘ın.
Motivated from the study of canonical systems or Sturm-Liouville
equations with a singular potential, and from other developments in the
indefinite world, it was a long standing open problem to find an indefinite
(Pontryagin space) analogue of the notion of canonical systems, and to
prove a corresponding analogue of de Branges´ Inverse Spectral Theorem.
We gave a definition of an indefinite analogue of a Hamiltonian function
and elaborated the operator theory of such `indefinite canoncial systems´
in previous work. In the present paper we prove the corresponding version
of the Inverse Spectral Theorem.
canonical system, Pontryagin space, Inverse Spectral Theorem
Electronic version of the publication:
Created from the Publication Database of the Vienna University of Technology.