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Scattering on the line via singular approximation

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 نشر من قبل Peter Gibson
 تاريخ النشر 2021
  مجال البحث فيزياء
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 تأليف Peter C. Gibson




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Motivated by applications to acoustic imaging, the present work establishes a framework to analyze scattering for the one-dimensional wave, Helmholtz, Schrodinger and Riccati equations that allows for coefficients which are more singular than can be accommodated by previous theory. In place of the standard scattering matrix or the Weyl-Titchmarsh $m$-function, the analysis centres on a new object, the generalized reflection coefficient, which maps frequency (or the spectral parameter) to automorphisms of the Poincare disk. Purely singul



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