On spectrum of strings with δ'-like perturbations of mass density

Yuriy Golovaty

Анотація


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 ε2h(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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DOI: http://dx.doi.org/10.30970/vmm.2020.89.060-079

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