Inverse scattering problem for Sturm-Liouville operator on non-compact A-graph. Uniqueness result.

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Published: Dec 22, 2015
DOI: https://doi.org/10.5556/j.tkjm.46.2015.1806
Keywords:
Sturm-Liouville operators noncompact graph graph with a cycle scattering problems inverse spectral problems

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Mikhail Ignatyev

Abstract

We consider a connected metric graph with the following property: each two cycles can have at most one common point. Such graphs are called A-graphs. On noncompact A-graph we consider a scattering problem for Sturm--Liouville differential operator with standard matching conditions in the internal vertices. Transport, spectral and scattering problems for differential operators on graphs appear frequently in mathematics, natural sciences and engineering. In particular, direct and inverse problems for such operators are used to construct and study models in mechanics, nano-electronics, quantum computing and waveguides. The most complete results on (both direct and inverse) spectral problems were achieved in the case of Sturm--Liouville operators on compact graphs, in the noncompact case there are no similar general results. In this paper, we establish some properties of the spectral characteristics and investigate the inverse problem of recovering the operator from the scattering data. A uniqueness theorem for such inverse problem is proved.

Article Details

How to Cite
Ignatyev, M. (2015). Inverse scattering problem for Sturm-Liouville operator on non-compact A-graph. Uniqueness result. Tamkang Journal of Mathematics, 46(4), 401–422. https://doi.org/10.5556/j.tkjm.46.2015.1806
Issue
Vol. 46 No. 4 (2015)
Section
Papers
Author Biography

Mikhail Ignatyev

Department ofMathematics, Saratov State University, Astrakhanskaya 83, Saratov 410012, Russia. E-mail: ignatievmu@info.sgu.ru E-mail: mikkieram@gmail.com

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