Recovery of the m-function from spectral data for generalized Sturm–Liouville problems

The Sturm–Liouville problem −y″+qy=λy, y(0) cos α=y′(0) sin α, (y′/y)(1)=h(λ)/g(λ) is studied, where h and g are real polynomials. Generalized norming constants ρnk associated with eigenvalues Λn are defined and formulae are given for recovering the m-function from these constants. This leads to a uniqueness theorem for the associated inverse problem.