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Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2013, Volume 13, Issue 3, Pages 59–64
DOI: https://doi.org/10.18500/1816-9791-2013-13-3-59-64 (Mi isu424) 		 
Mathematics

Necessary and sufficient conditions for the solvability of the inverse problem for Sturm–Liouville operators with a nonintegrable singularity inside a finite interval

A. E. Fedoseev

Saratov State University, Russia, 410012, Saratov, Astrahanskaya st., 83
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DOI: https://doi.org/10.18500/1816-9791-2013-13-3-59-64
Abstract: The inverse spectral problem of recovering Sturm–Liouville operators on a finite interval with a nonintegrable Bessel-type singularity in an interior point from the given spectral data is studied. A corresponding uniqueness theorem is proved, a constructive procedure for the solution of the inverse problem is provided. Necessary and sufficient conditions for the solvability of the inverse problem are obtained.
Key words: Sturm–Liouville operators, inverse problems, nonintegrable singularity, Weyl function, spectral data.
Bibliographic databases:
Document Type: Article
UDC: 517.927
Language: Russian
Citation: A. E. Fedoseev, “Necessary and sufficient conditions for the solvability of the inverse problem for Sturm–Liouville operators with a nonintegrable singularity inside a finite interval”, Izv. Saratov Univ. Math. Mech. Inform., 13:3 (2013), 59–64
Citation in format AMSBIB
\Bibitem{Fed13}
\by A.~E.~Fedoseev
\paper Necessary and sufficient conditions for the solvability of the inverse problem for Sturm--Liouville operators with a~nonintegrable singularity inside a~finite interval
\jour Izv. Saratov Univ. Math. Mech. Inform.
\yr 2013
\vol 13
\issue 3
\pages 59--64
\mathnet{http://mi.mathnet.ru/isu424}
\crossref{https://doi.org/10.18500/1816-9791-2013-13-3-59-64}
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