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

Abstract

The regularized trace formula of first order for the ”weighted” Sturm-Liouville equation with point δ-interaction is obtained.

On the Uniqueness of Inverse Problems for ”weighted” Sturm-Liouville Operator With Delta Interaction

“…Notice that, we can understand problem (1), (3) as studying the equation −y ′′ + q(x)y = λρ(x)y, x ∈ (0, π) , (4) when ρ(x) = 1 + αδ(x − π 2 ), where δ(x) is the Dirac function (see [1]). In this aspect, various spectral problems for the equation ( 4) have been investigated in [7].…”