M. Langer, H. Woracek:
"A function space model for canonical systems with an inner singularity";
Acta Sci.Math. (Szeged),
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,
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.
Erstellt aus der Publikationsdatenbank der Technischen Universität Wien.