Langer, Matthias and Woracek, Harald
(2013)
*The exponential type of the fundamental solution of an indefinite Hamiltonian system.*
Complex Analysis and Operator Theory, 7 (1).
pp. 285-312.
ISSN 1661-8254

## Abstract

The fundamental solution of a Hamiltonian system whose Hamiltonian H is positive definite and locally integrable is an entire function of exponential type. Its exponential type can be computed as the integral over $\sqrt{det H}$. We show that this formula remains true in the indefinite (Pontryagin space) situation, where the Hamiltonian is permitted to have finitely many inner singularities. As a consequence, we obtain a statement on non-cancellation of exponential growth for a class of entire matrix functions.

Item type: | Article |
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ID code: | 35845 |

Keywords: | Hamiltonian system, exponential type, Pontryagin space, fundamental solution, indefinite, Probabilities. Mathematical statistics, Computational Theory and Mathematics, Computational Mathematics, Applied Mathematics |

Subjects: | Science > Mathematics > Probabilities. Mathematical statistics |

Department: | Faculty of Science > Mathematics and Statistics |

Depositing user: | Pure Administrator |

Date Deposited: | 14 Nov 2011 10:58 |

Last modified: | 27 Mar 2014 09:50 |

URI: | http://strathprints.strath.ac.uk/id/eprint/35845 |

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