On the Scattering Problem and the Problem of Recovery of the Shape of a Graph
摘要
We consider a scattering problem generated by the Sturm–Liouville equation on a tree formed by an equilateral compact subtree with a lead (half-infinite edge) attached to this compact subtree. It is assumed that the potential on the lead is identically equal to zero and the potentials on finite edges are real L2-functions. It is shown how to determine the shape of the tree by using the S-function and the eigenvalues of the scattering problem.