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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.

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Metadaten
Author:Bert-Wolfgang SchulzeGND, Y. Wei
DOI:https://doi.org/10.1007/s11785-013-0289-3
ISSN:1661-8254 (print)
ISSN:1661-8262 (online)
Parent Title (English):Complex analysis and operator theory
Publisher:Springer
Place of publication:Basel
Document Type:Article
Language:English
Year of first Publication:2014
Year of Completion:2014
Release Date:2017/03/27
Volume:8
Issue:4
Pagenumber:39
First Page:803
Last Page:841
Funder: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