On characteristic functions of equilateral regular star-trees (Q402844)

This paper studies the spectral problem for a Sturm-Liouville operator on the edges of regular equilateral finite star-tree metric graphs, with Dirichlet conditions imposed on the pendant vertices, and continuity and Kirchhoff conditions at the interior vertices. The potential is assumed to be the same on each edge, and to be symmetric with respect to the mid-point. A characteristic function, that is an entire function whose zeros coincide with the eigenvalues of the problem, is constructed. Using this, a description of the spectrum of the problem is given.