# A local inverse spectral theorem for Hamiltonian systems

Langer, Matthias and Woracek, Harald
(2011)
*A local inverse spectral theorem for Hamiltonian systems.*
Inverse Problems, 27 (5).
ISSN 0266-5611

## Abstract

We consider (2×2)-Hamiltonian systems of the form $y'(x) = zJH(x)y(x)$, $x \in [s−, s+)$. If a system of this form is in the limit point case, an analytic function is associated with it, namely its Titchmarsh–Weyl coefficient q_H. The (global) uniqueness theorem due to de Branges says that the Hamiltonian H is (up to reparameterization) uniquely determined by the function q_H. In this paper we give a local uniqueness theorem; if the Titchmarsh–Weyl coefficients q_{H_1} and q_{H_2} corresponding to two Hamiltonian systems are exponentially close, then the Hamiltonians H_1 and H_2 coincide (up to reparameterization) up to a certain point of their domain, which depends on the quantitative degree of exponential closeness of the Titchmarsh–Weyl coefficients.

Item type: | Article |
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ID code: | 36014 |

Keywords: | inverse problems, conservation laws, scattering methods, uniqueness theorems, Probabilities. Mathematical statistics, Theoretical Computer Science |

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

Department: | Faculty of Science > Mathematics and Statistics |

Depositing user: | Pure Administrator |

Date Deposited: | 18 Nov 2011 05:22 |

Last modified: | 18 Nov 2016 03:32 |

URI: | http://strathprints.strath.ac.uk/id/eprint/36014 |

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