Inverse Spectral And Scattering Theory For The Half-Line Left-Definite Sturm-Liouville Problem
(2008) In SIAM Journal on Mathematical Analysis 40(5). p.2105-2131- Abstract
- The problem of integrating the Camassa-Holm equation leads to the scattering and inverse scattering problem for the Sturm-Liouville equation -u '' + 1/4 u = lambda wu, where w is a weight function which may change sign but where the left-hand side gives rise to a positive quadratic form so that one is led to a left-definite spectral problem. In this paper the spectral theory and a generalized Fourier transform associated with the equation -u '' + 1/4 u =lambda wu posed on a half-line are investigated. An inverse spectral theorem and an inverse scattering theorem are established. A crucial ingredient of the proofs of these results is a theorem of Paley-Wiener type which is shown to hold true. Additionally, the accumulation properties of... (More)
- The problem of integrating the Camassa-Holm equation leads to the scattering and inverse scattering problem for the Sturm-Liouville equation -u '' + 1/4 u = lambda wu, where w is a weight function which may change sign but where the left-hand side gives rise to a positive quadratic form so that one is led to a left-definite spectral problem. In this paper the spectral theory and a generalized Fourier transform associated with the equation -u '' + 1/4 u =lambda wu posed on a half-line are investigated. An inverse spectral theorem and an inverse scattering theorem are established. A crucial ingredient of the proofs of these results is a theorem of Paley-Wiener type which is shown to hold true. Additionally, the accumulation properties of eigenvalues are investigated. (Less)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/1375646
- author
- Bennewitz, Christer LU ; Brown, B. M. and Weikard, R.
- organization
- publishing date
- 2008
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- Camassa-Holm equation, Sturm-Liouville, problems, left-definite, inverse scattering problems, inverse spectral problems
- in
- SIAM Journal on Mathematical Analysis
- volume
- 40
- issue
- 5
- pages
- 2105 - 2131
- publisher
- Society for Industrial and Applied Mathematics
- external identifiers
-
- wos:000263103600016
- scopus:70350100726
- ISSN
- 0036-1410
- DOI
- 10.1137/080724575
- language
- English
- LU publication?
- yes
- id
- 3abb56cc-431e-4e1c-9147-4c804fee12c8 (old id 1375646)
- date added to LUP
- 2016-04-01 14:40:15
- date last changed
- 2022-01-28 01:52:37
@article{3abb56cc-431e-4e1c-9147-4c804fee12c8,
abstract = {{The problem of integrating the Camassa-Holm equation leads to the scattering and inverse scattering problem for the Sturm-Liouville equation -u '' + 1/4 u = lambda wu, where w is a weight function which may change sign but where the left-hand side gives rise to a positive quadratic form so that one is led to a left-definite spectral problem. In this paper the spectral theory and a generalized Fourier transform associated with the equation -u '' + 1/4 u =lambda wu posed on a half-line are investigated. An inverse spectral theorem and an inverse scattering theorem are established. A crucial ingredient of the proofs of these results is a theorem of Paley-Wiener type which is shown to hold true. Additionally, the accumulation properties of eigenvalues are investigated.}},
author = {{Bennewitz, Christer and Brown, B. M. and Weikard, R.}},
issn = {{0036-1410}},
keywords = {{Camassa-Holm equation; Sturm-Liouville; problems; left-definite; inverse scattering problems; inverse spectral problems}},
language = {{eng}},
number = {{5}},
pages = {{2105--2131}},
publisher = {{Society for Industrial and Applied Mathematics}},
series = {{SIAM Journal on Mathematical Analysis}},
title = {{Inverse Spectral And Scattering Theory For The Half-Line Left-Definite Sturm-Liouville Problem}},
url = {{http://dx.doi.org/10.1137/080724575}},
doi = {{10.1137/080724575}},
volume = {{40}},
year = {{2008}},
}