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 $X^2$. The extended 0-double space introduced by Lauter plays a useful role in the construction.

35 pages, 3 figures

References in corpus (1)

• Stability Estimates for the X-Ray Transform on Simple Asymptotically Hyperbolic Manifolds

Cited by in corpus (2)

• Microlocal analysis near null infinity in asymptotically flat spacetimes
• Biharmonic Maps Between Conformally Compact Manifolds