On spectrum of strings with $\delta'$-like perturbations of mass density

Yuriy Golovaty

doi:10.30970/vmm.2020.89.060-079

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arXiv · 2007.03259

On spectrum of strings with $\delta'$-like perturbations of mass density

Yuriy Golovaty

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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 $\delta'$-like sequence $\varepsilon^{-2}h(x/\varepsilon)$. 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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BibTeX RIS

Yuriy Golovaty. 2020-07-07. On spectrum of strings with $\delta'$-like perturbations of mass density. https://doi.org/10.30970/vmm.2020.89.060-079

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