2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/57635In this text we describe the spectral nature (pure point or continuous) of a self-similar Sturm-Liouville operator on the line or the half-line. This is motivated by the more general problem of understanding the spectrum of Laplace operators on unbounded finitely ramified self-similar sets. In this context, this furnishes the first example of a description of the spectral nature of the operator in the case where the so-called "Neumann-Dirichlet" eigenfunctions are absent.20 pages, 1 figureMathematical PhysicsDynamical Systems34L10 (34L20, 82B44)text