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Recovering a part of potential by partial information on spectra of boundary problems

Pivovarchik V.

Opuscula Mathematica

2005

Vol. 25, no. 1

131-137

Under additional conditions uniqueness of the solution is proved for the following problem. Given 1) the spectrum of the Dirichlet problem for the Sturm-Liouville equation on [0, a] with real potential q(x) mem L2(0, a), 2) a certain part of the spectrum of the Dirichlet problem for the same equation on [a/3, a] and 3) the potential on [0, a/3]. The aim is to find the potential on [a/3 ,a].