Anisotropic edge pseudo-differential operators with discrete asymptotics

An anisotropic pseudo-differential calculus aimed at solving parabolic differential and pseudo-differential equations in terms of Volterra pseudo-differential operators was studied by PIRIOU for Spatial variables on a closed C-infinity-manifold. Such a program also makes sense when the spatial variables run over a manifold with edges. Our approach deals with this case. It covers, in particular, manifolds with conical singularities. The main point of the present paper is the anisotropic edge pseudo-differential calculus, obtained as a substructure of our corresponding abstract anisotropic edge calculus with operator-valued symbols.