An Inverse Spectral Problem of Sturm–Liouville Problems with Transmission Conditions

Abstract

In this paper, a class of inverse Sturm–Liouville problems of Atkinson type with transmission conditions is investigated. Based on the method of well-known theory for inverse matrix eigenvalue problems and the spectral properties of Sturm–Liouville problems with transmission conditions of Atkinson type, the corresponding Sturm–Liouville problems can be constructed using two sets of interlacing real numbers and some other conditions. We solve the problems not only under the separated boundary conditions, but also under the real coupled boundary conditions and the general real self-adjoint transmission conditions.