[Back]

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.

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.

canonical system, Pontryagin space boundary triplet, maximal chain of

http://www.asc.tuwien.ac.at/preprint/2009/asc21x2009.pdf