On inverse problem for tree of Stieltjes strings

Abstract

For a given metric tree and two strictly interlacing sequences of numbers there exits a distribution of point masses on the edges (which are Stieltjes strings) such that one of the sequences is the spectrum of the   spectral problem  with the Neumann condition at the root of the tree while the second sequence is the spectrum of the   spectral problem with the Dirichlet condition at the root.