科研之友
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摘要
We consider (2x2)-Hamiltonian systems of the form y'(x) = zJH(x)y(x), x is an element of [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(H1) and q(H2) 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.
- 出版日期2011-5
