The Mellin-edge quantisation for corner operators
- 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 (Osaka J. Math. 37:221-260, 2000) 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.
Author details: | Bert-Wolfgang SchulzeGND, Y. Wei |
---|---|
DOI: | https://doi.org/10.1007/s11785-013-0289-3 |
ISSN: | 1661-8254 |
ISSN: | 1661-8262 |
Title of parent work (English): | Complex analysis and operator theory |
Publisher: | Springer |
Place of publishing: | Basel |
Publication type: | Article |
Language: | English |
Year of first publication: | 2014 |
Publication year: | 2014 |
Release date: | 2017/03/27 |
Volume: | 8 |
Issue: | 4 |
Number of pages: | 39 |
First page: | 803 |
Last Page: | 841 |
Funding institution: | NSFC (National Science Foundation of China) [11001135]; TSTC [10JCYBJC25200]; DFG (Deutsche Forschungsgemeinschaft) within the project "Partial Differential Equations in Geometry and Mathematical Physics"; Chern Institute of Mathematics in Tianjin, China; Research Grant at the Nankai University |
Organizational units: | Mathematisch-Naturwissenschaftliche Fakultät / Institut für Mathematik |
Peer review: | Referiert |