The Mellin-Edge Quantisation for Corner Operators
Abstract
We establish a quantisation of corner-degenerate symbols, here called Mellin-edge quantisation, on a manifold with second order singularities. The typical ingredients come from the "most singular" stratum of which is a second order edge where the infinite transversal cone has a base that is itself a manifold with smooth edge. The resulting operator-valued amplitude functions on the second order edge are formulated purely in terms of Mellin symbols taking values in the edge algebra over In this respect our result is formally analogous to a quantisation rule of a joint paper with J. Gil and J. Seiler for the simpler case of edge-degenerate symbols that corresponds to the singularity order 1. However, from the singularity order 2 on there appear new substantial difficulties for the first time, partly caused by the edge singularities of the cone over that tend to infinity.
Cite
@article{arxiv.1201.6525,
title = {The Mellin-Edge Quantisation for Corner Operators},
author = {Bert-Wolfgang Schulze and Yawei Wei},
journal= {arXiv preprint arXiv:1201.6525},
year = {2012}
}