2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/161618Let $\Hn$ be the $(2n+1)$-dimensional Heisenberg group and $K$ a compact group of automorphisms of $\Hn$ such that $(K\ltimes \Hn,K)$ is a Gelfand pair. We prove that the Gelfand transform is a topological isomorphism between the space of $K$-invariant Schwartz functions on $\Hn$ and the space of Schwartz function on a closed subset of $\R^s$ homeomorphic to the Gelfand spectrum of the Banach algebra of $K$-invariant integrable functions on $\Hn$.28 pagesFunctional AnalysisClassical Analysis and ODEs43A80 (Primary); 22E25 (Secondary)text