Duality for an indefinite inverse Sturm-Liouville problem

In this paper we solve an inverse spectral problem associated with a traditional Sturm-Liouville equation with an indefinite weight function. Specifically, we reconstruct a unique positive potential from two spectral sequences, given a weight function with a simple turning point in the interior of a finite interval with fixed end boundary conditions. We show the existence of special non-linear second order differential equations satisfied by these eigenvalue functions, dubbed the dual equations, eigenvalues whose asymptotics are used in the description of the reconstruction of the unknown potential. (c) 2005 Elsevier Inc. All rights reserved.