Inverse Spectral And Scattering Theory For The Half-Line Left-Definite Sturm-Liouville Problem
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 Four