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Elliptic parametrices in the 0-calculus of Mazzeo and Melrose

Peter Hintz

Vol. 5 (2023), No. 3, 729–766
DOI: 10.2140/paa.2023.5.729
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.

Keywords
uniformly degenerate operators, 0-calculus, elliptic parametrices, polyhomogeneous expansions
Mathematical Subject Classification
Primary: 35J75
Secondary: 35A17, 35C20
Milestones
Received: 25 September 2022
Revised: 17 December 2022
Accepted: 2 February 2023
Published: 24 August 2023
Authors
Peter Hintz
Department of Mathematics
ETH Zürich
Zürich
Switzerland