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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 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 finite-dimensional 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 splitting-and-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 significantly reduce the technical effort without losing sight of the essential ideas.

Original language | English |
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Pages (from-to) | 101-165 |

Number of pages | 65 |

Journal | Acta Scientiarum Mathematicarum |

Volume | 77 |

Issue number | 1-2 |

Publication status | Published - 2011 |

### Keywords

- space model
- canonical systems

## Fingerprint Dive into the research topics of 'A function space model for canonical systems'. Together they form a unique fingerprint.

## Projects

- 1 Finished

## Spectral Theory of Block Operator Matrices

EPSRC (Engineering and Physical Sciences Research Council)

1/09/07 → 30/11/09

Project: Research

## Cite this

Langer, M., & Woracek, H. (2011). A function space model for canonical systems.

*Acta Scientiarum Mathematicarum*,*77*(1-2), 101-165.