Inverse oscillation theory for Sturm–Liouville problems with non-separated boundary conditions

Abstract

A set of restrictions is given on the eigenvalues and their multiplicities, and on the oscillation counts of the eigenfunctions, for the beginning part of the spectrum of a Sturm–Liouville problem subject to self-adjoint boundary conditions of the form These restrictions are complete in the sense that if they are satisfied then an appropriate potential function q and boundary condition matrix K can be found generating the given spectral data.