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A partial inverse problem for the Sturm-Liouville operator on the lasso-graph

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  • The Sturm-Liouville operator with singular potentials on the lasso graph is considered. We suppose that the potential is known a priori on the boundary edge, and recover the potential on the loop from a part of the spectrum and some additional data. We prove the uniqueness theorem and provide a constructive algorithm for the solution of this partial inverse problem.

    Mathematics Subject Classification: 34A55, 34B05, 34B09, 34B45, 34L20, 34L40, 47E05.


    \begin{equation} \\ \end{equation}
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  • Figure 1.  Lasso graph

    Figure 2.  Plots for equation (7), $m = 5$

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