A 2-edge partial inverse problem for the Sturm-Liouville operators with singular potentials on a star-shaped graph

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Published: Mar 25, 2018
DOI: https://doi.org/10.5556/j.tkjm.49.2018.2425
Keywords:
Partial Inverse Problem Quantum Graph Sturm-Liouville Operator Singular Potential Weyl Function Riesz Basis

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Natalia Pavlovna Bondarenko

Abstract

Boundary value problems for Sturm-Liouville operators with potentials from the class $W_2^{-1}$ on a star-shaped graph are considered. We assume that the potentials are known on all the edges of the graph except two, and show that the potentials on the remaining edges can be constructed by fractional parts of two spectra. A uniqueness theorem is proved, and an algorithm for the constructive solution of the partial inverse problem is provided. The main ingredient of the proofs is the Riesz-basis property of specially constructed systems of functions.

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How to Cite
Bondarenko, N. P. (2018). A 2-edge partial inverse problem for the Sturm-Liouville operators with singular potentials on a star-shaped graph. Tamkang Journal of Mathematics, 49(1), 49–66. https://doi.org/10.5556/j.tkjm.49.2018.2425
Issue
Vol. 49 No. 1 (2018)
Section
Papers
Author Biography

Natalia Pavlovna Bondarenko

Department of Applied Mathematics, Samara National Research University, 34, Moskovskoye Shosse, Samara443086, Russia. Department of Mechanics andMathematics, Saratov State University, Astrakhanskaya 83, Saratov 410012, Russia.

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