2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/71704We show that a subspace $S$ of the space of real analytical functions on a manifold that satisfies certain regularity properties is contained in the set of solutions of a linear elliptic differential equation. The regularity properties are that $S$ is closed in $L^2(M)$ and that if a sequence of functions $f_n$ in $S$ converges in $L^2(M)$, then so do the partial derivatives of the functions $f_n$.6 pages, no figures, no tablesDifferential Geometry58J05, 32C05text