2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/148823We build a longitudinally smooth differentiable groupoid associated to any manifold with corners. The pseudodifferential calculus on this groupoid coincides with the pseudodifferential calculus of Melrose (also called b-calculus). We also define an algebra of rapidly decreasing functions on this groupoid; it contains the kernels of the smoothing operators of the (small) b-calculus.12 pages, LaTeX. This is a slight update from funct-an/9707008 (a citation was missing)Functional AnalysisOperator Algebras35S15, 47G30, 22A22 (Primary); 46L80, 19K56 (Secondary)text