2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/79142The fundamental solution for the wave equation in n variables is built from the simple one-dimensional formula, via an integral representation of the cosine of the sum of squares of self-adjoint operators. Representation formulas are given both in the commutative and non-commutative case. The formulas are illustrated for the wave equation as well as for the Klein-Gordon equati on. As examples for the non-commuting case, we discuss the harmonic oscillator and simple sum of squares hypoelliptic operators such as the Grushin operator and the Heisenberg Laplacian.Latex2eAnalysis of PDEsFunctional Analysis35L15 (Primary) 35C99 35L05 47D03 (Secondary)text