08-71 Sergei Avdonin and Victor Mikhaylov

The boundary control approach to inverse spectral theory (258K, Adobe PDF) Apr 3, 08

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Abstract. We establish connections between four approaches to inverse spectral problems: the classical Gelfand--Levitan theory, the Simon theory, the approach proposed by Remling, and the Boundary Control method. We show that the Boundary Control approach provides simple and physically motivated proofs of the central results of other theories. We demonstrate also the connections between the dynamical and spectral data and derive the local version of the classical Gelfand--Levitan equations.

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