In this study, we obtain a formula for the regularized trace formula for "weighted" Sturm--Liouville equation with point $\delta $- 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.
"A regularized trace formula for "weighted" Sturm-Liouville equation with point delta-interaction,"
Turkish Journal of Mathematics: Vol. 45:
4, Article 22.
Available at: https://journals.tubitak.gov.tr/math/vol45/iss4/22