turkmath.org

In this talk, we study the inverse problem of recovering a metric tree from the knowledge of the Dirichlet-to-Neumann matrix associtaed with the Laplacian. We prove an explicit formula which relates this matrix to the pairwise weighted distances of the leaves of the tree and, thus, allows us to recover the weighed tree. This result can be viewed as a counterpart of the Calderón problem in the analysis of PDEs. In contrast to earlier results on inverse problems for metric graphs, we only assume knowledge of the Dirichlet-to-Neumann matrix for a fixed energy, not of a whole matrix-valued function.