A uniqueness result for one-dimensional inverse scattering

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Abstract

We consider the whole-line inverse scattering problem for Sturm-Liouville equations which have constant coefficients on a half-line. Since in this case the reflection coefficient determines a Weyl-Titchmarsh m-function, it determines the coefficients up to some simple Liouville transformations. Given inverse spectral theory, proofs are fairly simple but provide extensions of known results as we require less smoothness and less decay than is customary.

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Subject classification (UKÄ) – MANDATORY

  • Mathematics

Keywords

  • Inverse scattering, m-function, one-dimensional problems, left and right, definite problems, MSC (2010) 34K29
Original languageEnglish
Pages (from-to)941-948
JournalMathematische Nachrichten
Volume285
Issue number8-9
Publication statusPublished - 2012
Publication categoryResearch
Peer-reviewedYes