Abstract
We study the asymptotic behaviour of eigenvalues and eigenfunctions of a boundary value problem for the Sturm-Liouville operator with general boundary conditions and the weight function perturbed by the so-called δ ' -like sequence ε 2 h ( x / ε ) . The eigenvalue problem is realized as a family of non-self-adjoint matrix operators acting on the same Hilbert space and the norm resolvent convergence of this family is established. We also prove the Hausdorff convergence of the perturbed spectra.
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