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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 

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
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Projects
 1 Finished

Spectral Theory of Block Operator Matrices
EPSRC (Engineering and Physical Sciences Research Council)
1/09/07 → 30/11/09
Project: Research