Inverse Sturm-Liouville spectral problem on symmetric star-tree

Abstract

A spectral problem for the Sturm–Liouville equation on the edges of an equilateral regular star-tree with the Dirichlet boundary conditions at the pendant vertices and Kirchhoff and continuity conditions at the interior vertices is considered. The potential in the Sturm–Liouville equation is a real–valued square summable function, symmetrically distributed with respect to the middle point of any edge. If {λj}is a sequence of real numbers, necessary and sufficient conditions for {λj}to be the spectrum of the problem under consideration are established. Copyright © 2013 John Wiley & Sons, Ltd.