Inverse Sturm–Liouville spectral problem on symmetric star‐tree

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 {λ_j}is a sequence of real numbers, necessary and sufficient conditions for {λ_j}to be the spectrum of the problem under consideration are established. Copyright © 2013 John Wiley & Sons, Ltd.