Pozitif Yarı Eksende Süreksizlik Koşuluna Sahip Sturm-Liouville Operatörünün Ters Saçılma Problemi

Abstract

In this paper, we consider the inverse scattering problem for Sturm-Liouville operator with discontinuity conditions at some point on the positive half line. The scattering data of this boundary value problem is examined. The resolvent operator is constructed and the expansion formula with respect to the eigenfunctions of this boundary value problem is obtained. The main equation or modified Marchenko equation of the inverse scattering problem is derived and an algorithm of the construction of the potential function according to scattering data of this boundary value problem is given.