Distribution of the Spectrum of a Sturm–Liouville Operator Perturbed by a Delta Interaction

In the Hilbert space \(L^2[0,+\infty )\) , weconsider the perturbation of a Sturm–Liouville operator by a Dirac delta function. A smoothpotential growing at infinity ensures the discreteness of the spectrum of the unperturbed operator.The distribution of eigenvalues of the perturbed operator is found, and the eigenvalue asymptoticsis established as a function of the perturbation parameters.