Elliptic parametrices in the 0-calculus of Mazzeo and Melrose
Abstract
The purpose of this note is to spell out the details of the construction of parametrices for fully elliptic uniformly degenerate pseudodifferential operators on manifolds X with boundary. Following the original work by Mazzeo-Melrose on the 0-calculus, the parametrices are shown to have (polyhomogeneous) conormal Schwartz kernels on the 0-double space, a resolution of X2. The extended 0-double space introduced by Lauter plays a useful role in the construction.
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