Pontryagin spaces of entire functions. V

Abstract

The spectral theory of a two-dimensional canonical (or ‘Hamiltonian’) 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 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 functionsMotivated 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. respectively.