Contributions to Books:
M. Langer, H. Woracek:
"A function space model for canonical systems with an inner singularity";
in: "ASC Report30/2009",
issued by: Institute for Analysis and Scientific Computing;
Vienna University of Technology,
Recently, a generalization to the Pontryagin space setting of the notion of
canonical (Hamiltonian) systems which involves a nite number of inner
singularities has been given. The spectral theory of inde nite canonical
systems was investigated with help of an operator model. This model
consists of a Pontryagin space boundary triple and was constructed in an
abstract way. Moreover, the construction of this operator model involves
a procedure of splitting-and-pasting which is technical but at the present
stage of development in general inevitable.
In this paper we provide an isomorphic form of this operator model
which acts in a nite dimensional extension of a function space naturally
associated with the given inde nite canonical system. We give explicit
formulae for the model operator and the boundary relation. Moreover, we
show that under certain asymptotic hypotheses the procedure of splittingand-
pasting can be avoided by employing a limiting process.
We restrict attention to the case of one singularity. This is the core of
the theory, and by making this restriction we can signi cantly reduce the
technical e ort without losing sight of the essential ideas.
Canonical system, Pontryagin space, boundary triple
Electronic version of the publication:
Created from the Publication Database of the Vienna University of Technology.