2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/146184In this paper we extend the notions of Schwartz functions, tempered functions and generalized Schwartz functions to Nash (i.e. smooth semi-algebraic) manifolds. We reprove for this case classically known properties of Schwartz functions on $R^n$ and build some additional tools which are important in representation theory.35 pages, LaTex. v3:minor changes + reference to results of duClouxAlgebraic GeometryRepresentation Theory14P20; 46F99text