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Abstract
Recently, a generalization to the Pontryagin space setting of the notion of canonical (Hamiltonian) systems which involves a finite number of inner singularities has been given. The spectral theory of indefinite 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 splittingandpasting 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 finitedimensional extension of a function space naturally associated with the given indefinite 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 splittingandpasting 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 significantly reduce the technical effort without losing sight of the essential ideas.
Original language  English 

Pages (fromto)  101165 
Number of pages  65 
Journal  Acta Scientiarum Mathematicarum 
Volume  77 
Issue number  12 
Publication status  Published  2011 
Keywords
 space model
 canonical systems
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 1 Finished

Spectral Theory of Block Operator Matrices
EPSRC (Engineering and Physical Sciences Research Council)
1/09/07 → 30/11/09
Project: Research