Asymptotic stability of the spectra of generalized indefinite strings
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866915041867988992 |
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| author | Xu, Guixin Zhang, Meirong Zhou, Zhe |
| author_facet | Xu, Guixin Zhang, Meirong Zhou, Zhe |
| contents | This paper focuses on the asymptotic stability of the spectra of generalized indefinite strings (GISs). A unitarily equivalent linear relation is introduced for GISs. It is shown that the solutions of the corresponding differential equations are continuously dependent on distributions and measures under certain conditions. Using these results, the convergence of unitarily equivalent linear relations for GISs is discussed. By the perturbation theory to closed linear relations, an asymptotic stability result concerning the spectra of linear relations for GISs is obtained. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_00022 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Asymptotic stability of the spectra of generalized indefinite strings Xu, Guixin Zhang, Meirong Zhou, Zhe Functional Analysis This paper focuses on the asymptotic stability of the spectra of generalized indefinite strings (GISs). A unitarily equivalent linear relation is introduced for GISs. It is shown that the solutions of the corresponding differential equations are continuously dependent on distributions and measures under certain conditions. Using these results, the convergence of unitarily equivalent linear relations for GISs is discussed. By the perturbation theory to closed linear relations, an asymptotic stability result concerning the spectra of linear relations for GISs is obtained. |
| title | Asymptotic stability of the spectra of generalized indefinite strings |
| topic | Functional Analysis |
| url | https://arxiv.org/abs/2412.00022 |