On spectrum of strings with $δ'$-like perturbations of mass density
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arXiv
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| Format: | Preprint |
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2020
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| _version_ | 1866910915644882944 |
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| author | Golovaty, Yuriy |
| author_facet | Golovaty, Yuriy |
| contents | 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 $\varepsilon^{-2}h(x/\varepsilon)$. 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2007_03259 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | On spectrum of strings with $δ'$-like perturbations of mass density Golovaty, Yuriy Spectral Theory 34B24, 34L05, 34L10 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 $\varepsilon^{-2}h(x/\varepsilon)$. 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. |
| title | On spectrum of strings with $δ'$-like perturbations of mass density |
| topic | Spectral Theory 34B24, 34L05, 34L10 |
| url | https://arxiv.org/abs/2007.03259 |