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A uniqueness result for one-dimensional inverse scattering

Bennewitz, Christer LU ; Brown, B. M. and Weikard, R. (2012) In Mathematische Nachrichten 285(8-9). p.941-948
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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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Inverse scattering, m-function, one-dimensional problems, left and right, definite problems, MSC (2010) 34K29
in
Mathematische Nachrichten
volume
285
issue
8-9
pages
941 - 948
publisher
John Wiley & Sons
external identifiers
  • wos:000304524500004
  • scopus:84861706127
ISSN
0025-584X
DOI
10.1002/mana.201100101
language
English
LU publication?
yes
id
e1f9ed22-5b32-4ddb-a0c4-7a1a364e595d (old id 2896948)
date added to LUP
2012-07-24 10:57:52
date last changed
2017-01-01 03:07:49
@article{e1f9ed22-5b32-4ddb-a0c4-7a1a364e595d,
  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.},
  author       = {Bennewitz, Christer and Brown, B. M. and Weikard, R.},
  issn         = {0025-584X},
  keyword      = {Inverse scattering,m-function,one-dimensional problems,left and right,definite problems,MSC (2010) 34K29},
  language     = {eng},
  number       = {8-9},
  pages        = {941--948},
  publisher    = {John Wiley & Sons},
  series       = {Mathematische Nachrichten},
  title        = {A uniqueness result for one-dimensional inverse scattering},
  url          = {http://dx.doi.org/10.1002/mana.201100101},
  volume       = {285},
  year         = {2012},
}