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St. Petersburg Mathematical Journal
St. Petersburg Mathematical Journal
ISSN 1547-7371(online) ISSN 1061-0022(print)

   

 

The inverse Sturm-Liouville problem with mixed boundary conditions


Authors: E. Korotyaev and D. Chelkak
Translated by: the authors
Original publication: Algebra i Analiz, tom 21 (2009), nomer 5.
Journal: St. Petersburg Math. J. 21 (2010), 761-778
MSC (2010): Primary 34B24
Published electronically: July 15, 2010
MathSciNet review: 2604565
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Abstract | References | Similar Articles | Additional Information

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.


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Additional Information

E. Korotyaev
Affiliation: School of Mathematics, Cardiff University, Senghennydd Road, CF24 4AG Cardiff, Wales, United Kingdom
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

DOI: http://dx.doi.org/10.1090/S1061-0022-2010-01116-6
Keywords: Inverse spectral theory, Sturm–Liouville operators
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)
Article copyright: © Copyright 2010 American Mathematical Society