Abstract
In this article, we consider a spectral problem generated by the Sturm–Liouville equation on the edges of an equilateral regular tree. It is assumed that the Dirichlet boundary conditions are imposed at the pendant vertices and continuity and Kirchhoff's conditions at the interior vertices. The potential in the Sturm–Liouville equations, the same on each edge, is real, symmetric with respect to the middle of an edge and belongs to L 2(0, a) where a is the length of an edge. Conditions are obtained on a sequence of real numbers necessary and sufficient to be the spectrum of the considered spectral problem.
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