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Publications in Scientific Journals:

M. Kaltenbäck, H. Woracek:
"Pontryagin spaces of entire functions. V";
Acta Sci.Math. (Szeged), 77 (2011), 223 - 336.



English abstract:
The spectral theory of a two-dimensional canonical (or `Hamilto-
nian´) system is closely related with two notions, depending whether Weyl´s
limit circle or limit point case prevails. 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 mul-
tiplication 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 equa-
tions 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 mon-
odromy matrix or Weyl coefficient, respectively, and of the Fourier transform.

Created from the Publication Database of the Vienna University of Technology.