  We discuss direct and inverse spectral theory of self-adjoint Sturm-Liouville
relations with separated boundary conditions in the left-definite setting. In
particular, we develop singular Weyl-Titchmarsh theory for these relations.
Consequently, we apply de Branges' subspace ordering theorem to obtain inverse
uniqueness results for the associated spectral measure. The results can be
applied to solve the inverse spectral problem associated with the Camassa-Holm
equation.
