Mathematical Sciences

Lund University

Title A uniqueness result for one-dimensional inverse scattering
Authors Christer Bennewitz, B. M. Brown, R. Weikard
Alternative Location, Restricted Access
Publication Mathematische Nachrichten
Year 2012
Volume 285
Issue 8-9
Pages 941 - 948
Document type Article
Status Published
Quality controlled Yes
Language eng
Publisher Wiley-V C H Verlag Gmbh
Abstract English 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.
Keywords Inverse scattering, m-function, one-dimensional problems, left and right, definite problems, MSC (2010) 34K29,
ISBN/ISSN/Other ISSN: 0025-584X