Langer, Matthias and Woracek, H. (2011) A function space model for canonical systems. Acta Scientiarum Mathematicarum, 77 (12). pp. 101165.

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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.
Item type:  Article 

ID code:  35931 
Keywords:  space model , canonical systems, Probabilities. Mathematical statistics, Analysis, Applied Mathematics 
Subjects:  Science > Mathematics > Probabilities. Mathematical statistics 
Department:  Faculty of Science > Mathematics and Statistics 
Depositing user:  Pure Administrator 
Date Deposited:  16 Nov 2011 14:46 
Last modified:  15 Apr 2015 12:40 
URI:  http://strathprints.strath.ac.uk/id/eprint/35931 
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