The inverse Sturm–Liouville problem with mixed boundary conditions
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E. Korotyaev and D. Chelkak
Translated by: the authors - St. Petersburg Math. J. 21 (2010), 761-778
- DOI: https://doi.org/10.1090/S1061-0022-2010-01116-6
- Published electronically: July 15, 2010
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Abstract:
Let $H\psi =-\psi ”+q\psi$, $\psi (0)=0$, $\psi ’(1)+b\psi (1)=0$ be a selfadjoint Sturm–Liouville operator acting in $L^2(0,1)$. Let $\lambda _n(q,b)$ and $\nu _n(q,b)$ denote its eigenvalues and the so-called norming constants, respectively. A complete characterization of all spectral data $(\{\lambda _n\}_{n=0}^{+\infty };\{\nu _n\}_{n=0}^{+\infty })$ corresponding to $(q;b)\in L^2(0,1)\times \mathbb {R}$ is given, together with a similar characterization for fixed $b$ and a parametrization of isospectral manifolds.References
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Bibliographic Information
- E. Korotyaev
- Affiliation: School of Mathematics, Cardiff University, Senghennydd Road, CF24 4AG Cardiff, Wales, United Kingdom
- MR Author ID: 211673
- Email: korotyaev@gmail.com
- D. Chelkak
- Affiliation: Department of Mathematics and Mechanics, St. Petersburg State University, Universitetskii Prospekt 28, Staryi Petergof, St. Petersburg 198504, Russia
- Email: dchelkak@pdmi.ras.ru
- Received by editor(s): March 15, 2008
- Published electronically: July 15, 2010
- Additional Notes: The first author was partially supported by EPSRC, grant EP/D054621
The second author was partially supported by the Foundation of the President of the Russian Federation (grants no. MK-4306.2008.1 and NSh-2409.2008.1) - © Copyright 2010 American Mathematical Society
- Journal: St. Petersburg Math. J. 21 (2010), 761-778
- MSC (2010): Primary 34B24
- DOI: https://doi.org/10.1090/S1061-0022-2010-01116-6
- MathSciNet review: 2604565