On inverse problem for singular Sturm-Liouville operator from two spectra
In the paper, an inverse problem with two given spectra for second order differential operator with singularity of type $\cfrac{2}{r} + \cfrac{l(l+1)}{r^2}$ (here, $l$ is a positive integer or zero) at zero point is studied. It is well known that two spectra $\{\lambda_n\}$ and $\{\mu_n\}$ uniquely...
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| Datum: | 2006 |
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| Hauptverfasser: | , , , |
| Format: | Artikel |
| Sprache: | Englisch |
| Veröffentlicht: |
Institute of Mathematics, NAS of Ukraine
2006
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| Online Zugang: | https://umj.imath.kiev.ua/index.php/umj/article/view/3440 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
| Завантажити файл: |  |
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Ukrains’kyi Matematychnyi Zhurnal| Zusammenfassung: | In the paper, an inverse problem with two given spectra for second order differential operator with singularity
of type $\cfrac{2}{r} + \cfrac{l(l+1)}{r^2}$
(here, $l$ is a positive integer or zero) at zero point is studied. It is well known that
two spectra $\{\lambda_n\}$ and $\{\mu_n\}$ uniquely determine the potential function $q(r)$ in a singular Sturm-Liouville equation defined on interval $(0, \pi]$.
One of the aims of the paper is to prove the generalized degeneracy of the kernel $K(r, s)$. In particular, we obtain a new proof of Hochstadt's theorem concerning the structure of the difference $\widetilde{q}(r) - q(r)$. |
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