Uniform stability of recovering the Sturm-Liouville operator on a star-graph

Abstract

In the paper, we study the problem of recovering the Sturm-Liouville operator on a star-graph from the Weyl vector. It generalizes the problem of recovering the classical Sturm-Liouville operator on an interval from the Weyl function, and the problems of recovering from other spectral data can be reduced to this problem. The uniqueness and the constructive method for solving the problem under study were previously obtained by V.A. Yurko in the case of a tree (Inverse Problems, 2005). Here, we prove its uniform stability, which includes Lipschitz estimates with a constant depending only on the number bounding the norms of the potentials. Stability results are necessary for justifying the well-posedness of the problem statement, and they are important for developing numerical methods. As auxiliary results, we obtain the uniform stability of the direct problem, as well as the uniform stability of the partial derivatives of the transmutation operator kernel related to the classical Sturm-Liouville operator.