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Inverse spectral-scattering problem for the Sturm-Liouville operator on a noncompact star-type graph. (English) Zbl 1292.34011

The authors consider a selfadjoint Sturm-Liouville operator on a noncompact star-type graph, possessing more than one infinite edge, under the standard matching conditions in the internal vertex. In the boundary vertices, Robin-type boundary conditions are imposed. The authors introduce the so-called spectral-scattering data, which generalize the classical spectral data for the Sturm-Liouville operator on the half-line or a finite interval and the classical scattering data of the Sturm-Liouville operator on the line. Using the method of spectral mappings, they prove a uniqueness theorem on recovering the Sturm-Liouville operator on the graph from these spectral-scattering data.

MSC:

34A55 Inverse problems involving ordinary differential equations
34B24 Sturm-Liouville theory
34B45 Boundary value problems on graphs and networks for ordinary differential equations
34B40 Boundary value problems on infinite intervals for ordinary differential equations
47E05 General theory of ordinary differential operators
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