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A partial inverse Sturm‐Liouville problem on an arbitrary graph
Author(s) -
Bondarenko Natalia P.
Publication year - 2021
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.7231
Subject(s) - mathematics , sturm–liouville theory , inverse problem , uniqueness , graph , boundary value problem , inverse , uniqueness theorem for poisson's equation , mathematical analysis , discrete mathematics , geometry
The Sturm‐Liouville operator with singular potentials of classW 2 − 1on a graph of arbitrary geometrical structure is considered. We study the partial inverse problem, which consists in the recovery of the potential on a boundary edge of the graph from a subspectrum under the assumption that the potentials on the other edges are known a priori. We obtain (i) the uniqueness theorem, (ii) a reconstruction algorithm, (iii) global solvability, and (iv) local solvability and stability for this inverse problem. Our method is based on reduction of the partial inverse problem on a graph to the Sturm‐Liouville problem on a finite interval with entire analytic functions in the boundary condition.