| Title | Inverse Spectral And Scattering Theory For The Half-Line Left-Definite Sturm-Liouville Problem |
| Authors | Christer Bennewitz, B. M. Brown, R. Weikard |
| Alternative Location | http://dx.doi.org/10.1137/0..., Restricted Access |
| Publication | Siam Journal On Mathematical Analysis |
| Year | 2008 |
| Volume | 40 |
| Issue | 5 |
| Pages | 2105 - 2131 |
| Document type | Article |
| Status | Published |
| Quality controlled | Yes |
| Language | eng |
| Publisher | Siam Publications |
| Abstract English | 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. |
| Keywords | Camassa-Holm equation, Sturm-Liouville, problems, left-definite, inverse scattering problems, inverse spectral problems, |
| ISBN/ISSN/Other | ISSN: 0036-1410 |
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