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.
Verfasserangaben: | Bert-Wolfgang SchulzeGND, Y. Wei |
---|---|
DOI: | https://doi.org/10.1007/s11785-013-0289-3 |
ISSN: | 1661-8254 |
ISSN: | 1661-8262 |
Titel des übergeordneten Werks (Englisch): | Complex analysis and operator theory |
Verlag: | Springer |
Verlagsort: | Basel |
Publikationstyp: | Wissenschaftlicher Artikel |
Sprache: | Englisch |
Jahr der Erstveröffentlichung: | 2014 |
Erscheinungsjahr: | 2014 |
Datum der Freischaltung: | 27.03.2017 |
Band: | 8 |
Ausgabe: | 4 |
Seitenanzahl: | 39 |
Erste Seite: | 803 |
Letzte Seite: | 841 |
Fördernde 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 |
Organisationseinheiten: | Mathematisch-Naturwissenschaftliche Fakultät / Institut für Mathematik |
Peer Review: | Referiert |