A regularized trace formula for ”weighted” Sturm-Liouville equation with point δ - interaction

Abstract

In this study, we obtain a formula for the regularized trace formula for ”weighted” Sturm–Liouville equation with point δ - interaction. At the begining, for the correct determination of solutions of analyzed equation at the point of discontinuty, the matching conditions are required. As a result, an equation is derived for the eigenvalues of the differential operator given in this study.