A partial inverse problem for the Sturm-Liouville operator on a star-shaped graph

2017/01/01 by Bondarenko, Natalia · 6 citations
#FOS: Mathematics #Spectral Theory (math.SP)

paper · doi:10.48550/arxiv.1701.00219

Abstract

The Sturm-Liouville operator on a star-shaped graph is considered. We assume that the potential is known a priori on all the edges except one, and study the partial inverse problem, which consists in recovering the potential on the remaining edge from the part of the spectrum. A constructive method is developed for the solution of this problem, based on the Riesz-basicity of some sequence of vector functions. The local solvability of the inverse problem and the stability of its solution are proved.

Cited by

• Stability of the inverse Sturm-Liouville problem on a graph with a cycle
• Uniqueness of Inverse Spectral Problem of Non-Local Sturm-Liouville Operators on Star Graph
• Topology in One Point Interaction Problem on Extended Non-Local Star Graphs and its Eigenvalues
• Recovering the Topology in One Point Interaction Problem on Extended Non-Local Star Graphs
• Partial Inverse Spectral Problems for Sturm-Liouville Operators with Frozen Arguments on a Star-Shaped Graph
• Uniform stability for the matrix inverse Sturm-Liouville problems

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