Elliptic parametrices in the 0-calculus of Mazzeo and Melrose

Abstract

We present a detailed construction of parametrices for fully elliptic uniformly degenerate differential or pseudodifferential operators on manifolds X with boundary. Following the original work by Mazzeo and Melrose on the 0-calculus, the parametrices are shown to have (polyhomogeneous) conormal Schwartz kernels on the 0-double space, which is a resolution of X². The extended 0-double space introduced by Lauter plays a useful role in the construction.