Inverse Spectral And Scattering Theory For The HalfLine LeftDefinite SturmLiouville Problem
(2008) In SIAM Journal on Mathematical Analysis 40(5). p.21052131 Abstract
 The problem of integrating the CamassaHolm equation leads to the scattering and inverse scattering problem for the SturmLiouville equation u '' + 1/4 u = lambda wu, where w is a weight function which may change sign but where the lefthand side gives rise to a positive quadratic form so that one is led to a leftdefinite 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 halfline 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 PaleyWiener type which is shown to hold true. Additionally, the accumulation properties of... (More)
 The problem of integrating the CamassaHolm equation leads to the scattering and inverse scattering problem for the SturmLiouville equation u '' + 1/4 u = lambda wu, where w is a weight function which may change sign but where the lefthand side gives rise to a positive quadratic form so that one is led to a leftdefinite 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 halfline 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 PaleyWiener 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:
http://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
 CamassaHolm equation, SturmLiouville, problems, leftdefinite, inverse scattering problems, inverse spectral problems
 in
 SIAM Journal on Mathematical Analysis
 volume
 40
 issue
 5
 pages
 2105  2131
 publisher
 SIAM
 external identifiers

 wos:000263103600016
 scopus:70350100726
 ISSN
 00361410
 DOI
 10.1137/080724575
 language
 English
 LU publication?
 yes
 id
 3abb56cc431e4e1c91474c804fee12c8 (old id 1375646)
 date added to LUP
 20160401 14:40:15
 date last changed
 20200112 16:47:10
@article{3abb56cc431e4e1c91474c804fee12c8, abstract = {The problem of integrating the CamassaHolm equation leads to the scattering and inverse scattering problem for the SturmLiouville equation u '' + 1/4 u = lambda wu, where w is a weight function which may change sign but where the lefthand side gives rise to a positive quadratic form so that one is led to a leftdefinite 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 halfline 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 PaleyWiener 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 = {00361410}, language = {eng}, number = {5}, pages = {21052131}, publisher = {SIAM}, series = {SIAM Journal on Mathematical Analysis}, title = {Inverse Spectral And Scattering Theory For The HalfLine LeftDefinite SturmLiouville Problem}, url = {http://dx.doi.org/10.1137/080724575}, doi = {10.1137/080724575}, volume = {40}, year = {2008}, }