Operators with singular trace conditions on a manifold with edges

We establish a new calculus of pseudodifferential operators on a manifold with smooth edges and study ellipticity with extra trace and potential conditions (as well as Green operators) at the edge. In contrast to the known scenario with conditions of that kind in integral form we admit in this paper singular trace and Green operators. In contrast to standard conditions in the theory of elliptic boundary value problems (like Dirichlet or Neumann conditions) our singular trace conditions, in general, do not act on functions that are smooth up to the boundary, but admit a more general asymptotic structure. Their action is now associated with the Laurent coefficients of the meromorphic Mellin transforms of functions with respect to the half-axis variable, the distance to the edge.