TY - JOUR
A1 - Schulze, Bert-Wolfgang
A1 - Wei, Y.
T1 - The Mellin-edge quantisation for corner operators
JF - Complex analysis and operator theory
N2 - 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.
Y1 - 2014
U6 - http://dx.doi.org/10.1007/s11785-013-0289-3
SN - 1661-8254 (print)
SN - 1661-8262 (online)
VL - 8
IS - 4
SP - 803
EP - 841
PB - Springer
CY - Basel
ER -
TY - INPR
A1 - Schulze, Bert-Wolfgang
A1 - Wei, Y.
T1 - Edge-boundary problems with singular trace conditions
N2 - The ellipticity of boundary value problems on a smooth manifold with boundary relies on a two-component principal symbolic structure (σψ; σ∂), consisting of interior and boundary symbols. In the case of a smooth edge on manifolds with boundary we have a third symbolic component, namely the edge symbol σ∧, referring to extra conditions on the edge, analogously as boundary conditions. Apart from such conditions in integral form' there may exist singular trace conditions, investigated in [6] on closed' manifolds with edge. Here we concentrate on the phenomena in combination with boundary conditions and edge problem.
T3 - Preprint - (2008) 04
Y1 - 2008
U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-30317
ER -