M. Kaltenbäck, H. Woracek:

"Pontryagin spaces of entire functions. V";

Acta Sci.Math. (Szeged),77(2011), 223 - 336.

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.

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