2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/155411In this paper we use a unified way studying the decay estimate for a class of dispersive semigroup given by $e^{itϕ(\sqrt{-Δ})}$, where $ϕ: \mathbb{R}^+\to \mathbb{R}$ is smooth away from the origin. Especially, the decay estimates for the solutions of the Klein-Gordon equation and the beam equation are simplified and slightly improved.16 pages, 0 figureAnalysis of PDEsClassical Analysis and ODEs42B25; 35F20text