For citation:
Fedoseev A. E. Necessary and Sufficient Conditions for the Solvability of the Inverse Problem for Sturm–Liouville Operators with a Nonintegrable Singularity Inside a Finite Interval. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2013, vol. 13, iss. 3, pp. 59-64. DOI: 10.18500/1816-9791-2013-13-3-59-64
This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
Published online:
27.08.2013
Full text:
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Language:
Russian
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UDC:
517.927
Necessary and Sufficient Conditions for the Solvability of the Inverse Problem for Sturm–Liouville Operators with a Nonintegrable Singularity Inside a Finite Interval
Autors:
Fedoseev Alexey Evgen'evich, Saratov State University
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.
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References:
- Marchenko V. A. Sturm–Liouville operators and app- lications. Basel, Birkh¨user, 1986. 367 p. (Russ. ed.: Marchenko V. A. Operatory Shturma–Liuvillia i ikh prilozheniia. Kiev, Naukova Dumka, 1977. 331 p.)
- Levitan B. M. Inverse Sturm–Liouville problems. Utrecht, VNU, 1987, 240 p. (Russ. ed.: Levitan B. M. Obratnye zadachi Shturma–Liuvillia. Moscow, Nauka, 1984, 239 p.)
- Yurko V. A. Vvedenie v teoriiu obratnykh spekt- ral’nykh zadach [Introduction to the theory of inverse spectral problems]. Moscow, Fizmatlit, 1984, 384 p. (in Russian).
- Yurko V. A. Method of Spectral Mappings in the Inverse Problem Theory, Inverse and Ill-posed Problems Series. Utrecht, VSP, 2002, 303 p.
Received:
12.02.2013
Accepted:
18.07.2013
Published:
30.08.2013
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