Recovering of the Stiffness Coefficients of the Sturm–Liouville Operator on a Star Graph from a Finite Set of Its Eigenvalues

Baltabek Esmatovich Kanguzhin, Zhalgas Kaiyrbek, Mergul Mustafina

2024

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DOI 10.1134/s1995080224602881
Data confidence 70 medium
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Abstract

Abstract The paper identifies a class of self-adjoint Sturm–Liouville operators on a star graph with a simple spectrum. The matching conditions at the internal vertex of the graph contain a set of parameters. These parameters are interpreted as stiffness coefficients. The paper proves that a finite set of eigenvalues allows one to uniquely reconstruct a set of stiffness coefficients. The novelty of the work is the fact that it is enough to know a finite set of eigenvalues of the original problem to unique restore the required stiffness coefficients.