Sturm-Liouville with δ–interaction.

Abstract

This article describes the correct perturbed ordinary differential operators of second order in the punctured segment. And find a resolution perturbed. One obtained an asymptotic formula for the eigenvalues of the perturbed. This work is dedicated to the study of the properties of one-dimensional analogue of the Laplace operator. Trace theory of linear operators begins with the fundamental results Tata linear algebra, matrix trace of a linear operator is invariant to- respect to the choice of basis and coincides with the spectral trace. The role of this invariant and its consequences in various areas of algebra, analysis, Lisa, the geometry is very big. The problem of computing regularized traces back to the work of I.M. Gelfand and B.M. Levitan. They have been considered the Sturm-Liouville problem with Dirichlet boundary conditions. L.A. Diky in their work the regularized traces a regular Sturm-Liouville higher orders.