Half-inverse spectral problems for Sturm--Liouville operators with singular potentials

2003/12/09 by Rostyslav O. Hryniv, Yaroslav V. Mykytyuk · 3 citations
Mathematics · #math.SP #math.CA #msc:34A55 #msc:34B24 #msc:34L05

paper · pdf · doi:10.1088/0266-5611/20/5/006

published as Inverse Problems 20 (2004), no. 5, 1423 - 1444. · 21 pages

arxiv created 2003/12/09 · arxiv updated 2009/12/01

Abstract

Half-inverse spectral problem for a Sturm--Liouville operator consists in reconstruction of this operator by its spectrum and half of the potential. We give the necessary and sufficient conditions for solvability of the half-inverse spectral problem for the class of Sturm--Liouville operators with singular potentials from the space W^-1₂(0,1) and provide the reconstruction algorithm.

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