Contributions to Books:
M. Kaltenbäck, H. Woracek:
"Pontryagin spaces of entire functions V";
in: "ASC Report 21/2009",
issued by: Institute for Analysis and Scientific Computing;
Vienna University of Technology,
Wien,
2009,
ISBN: 978-3-902627-02-5.
English abstract:
The spectral theory of a two-dimensional canonical (or `Hamiltonian´)
system is closely related with two notions, depending whetherWeyl´s limit
circle or limit point case previals. Namely, with its monodromy matrix
or its Weyl coefficient, respectively. A Fourier transform exists which
relates the differential operator induced by the canonical system to the
operator of multiplication by the independent variable in a reproducing
kernel space of entire 2-vector valued functions or in a weighted L2-space
of scalar valued functions, respectively.
Motivated from the study of canonical systems or Sturm-Liouville
equations with a singular potential and from other developments in Pontryagin
space theory, we have suggested a generalization of canonical systems
to an indefinite setting which includes a finite number of inner singularities.
We have constructed an operator model for such `indefinite
canonical systems´. The present paper is devoted to the construction of
the corresponding monodromy matrix or Weyl coefficient, respectively,
and of the Fourier transform.
Keywords:
canonical system, Pontryagin space boundary triplet, maximal chain of
Electronic version of the publication:
http://www.asc.tuwien.ac.at/preprint/2009/asc21x2009.pdf
Created from the Publication Database of the Vienna University of Technology.