| Abstract: |
| The talk presents a result of recovering a differential operator from its spectral characteristics in the space of piecewise smooth functions on a star graph. The operator of the boundary value problem has a singularity generated by the structure of the graph. Differential expression is defined on the interior parts of all the edges of the graph. At an internal node of the graph the Kirchhoff-Neumann matching condition arises. The spectral approach is based on the spectral properties of an elliptic operator: the analyticity of the Green`s function for boundary value problem on the spectral parameter, spectral completeness and the bases property of the set of eigenfunctions in the space of square summable functions. The identifiability of a system is closely related to its controllability. |
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