Inverse scattering problem for a special class of canonical systems and non-linear Fourier integral. Part I: asymptotics of eigenfunctions
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en
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Este ítem está publicado en
Operator Theory: Advances and Applications. 2009, vol. 186, p. 285-324
Springer
Resumen en inglés
An original approach to the inverse scattering for Jacobi matrices was recently suggested in Volberg-Yuditskii [2002]. The authors considered quite sophisticated spectral sets (including Cantor sets of positive Lebesgue ...Leer más >
An original approach to the inverse scattering for Jacobi matrices was recently suggested in Volberg-Yuditskii [2002]. The authors considered quite sophisticated spectral sets (including Cantor sets of positive Lebesgue measure), however they did not take into account the mass point spectrum. This paper follows similar lines for the continuous setting with an absolutely continuous spectrum on the half-axis and a pure point spectrum on the negative half-axis satisfying the Blaschke condition. This leads us to the solution of the inverse scattering problem for a class of canonical systems that generalizes the case of Sturm-Liouville (Schrodinger) operator.< Leer menos
Palabras clave en italiano
Schrodinger operator
canonical differential system
inverse scattering
functional model
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