Projects per year
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 |
---|---|
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