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JOURNALS // Algebra i Analiz // Archive

Algebra i Analiz, 2009 Volume 21, Issue 5, Pages 114–137 (Mi aa1155)

This article is cited in 17 papers

Research Papers

The inverse Sturm–Liouville problem with mixed boundary conditions

E. L. Korotyaeva, D. S. Chelkakb

a School of Math., Cardiff University, Cardiff, Wales, UK
b St. Petersburg State University, Department of Mathematics and Mechanics, St. Petersburg, Russia

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.

MSC: 34B24

Received: 15.03.2008


 English version:
St. Petersburg Mathematical Journal, 2010, 21:5, 761–778

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