A uniqueness result for one-dimensional inverse scattering
(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.
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/2896948
- author
- Bennewitz, Christer LU ; Brown, B. M. and Weikard, R.
- organization
- publishing date
- 2012
- 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 Inc.
- 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
- 2016-04-01 09:56:19
- date last changed
- 2022-01-25 18:09:42
@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}}, keywords = {{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 Inc.}}, series = {{Mathematische Nachrichten}}, title = {{A uniqueness result for one-dimensional inverse scattering}}, url = {{http://dx.doi.org/10.1002/mana.201100101}}, doi = {{10.1002/mana.201100101}}, volume = {{285}}, year = {{2012}}, }