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### 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.

Original language | English |
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Article number | 055002 |

Number of pages | 17 |

Journal | Inverse Problems |

Volume | 27 |

Issue number | 5 |

DOIs | |

Publication status | Published - 29 Mar 2011 |

### Keywords

- inverse problems
- conservation laws
- scattering methods
- uniqueness theorems

## Fingerprint Dive into the research topics of 'A local inverse spectral theorem for Hamiltonian 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 local inverse spectral theorem for Hamiltonian systems.

*Inverse Problems*,*27*(5), [055002]. https://doi.org/10.1088/0266-5611/27/5/055002