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

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