%0 Journal Article %T Pseudodifferential calculus on manifolds with corners and groupoids %A Bertrand Monthubert %J Mathematics %D 1997 %I arXiv %X We 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. %U http://arxiv.org/abs/funct-an/9707008v2