Abstract
The Sturm–Liouville operator with singular potentials from the class \(W_2^{-1}\) is considered on a star-shaped graph with different edge lengths. We suppose that the potentials are known a priori on a part of the edges, and study the partial inverse problems, that consist in recovering the potentials on the other edges from a fractional part of the spectrum and some additional data. We prove three uniqueness theorems and provide a constructive algorithm for the solution of the inverse problems.
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Bondarenko, N.P., Yang, CF. Partial Inverse Problems for the Sturm–Liouville Operator on a Star-Shaped Graph with Different Edge Lengths. Results Math 73, 56 (2018). https://doi.org/10.1007/s00025-018-0817-6
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DOI: https://doi.org/10.1007/s00025-018-0817-6