TY  - JOUR
A1  - Rungrottheera, Wannarut
A1  - Schulze, Bert-Wolfgang
T1  - Weighted spaces on corner manifolds
JF  - Complex variables and elliptic equations
N2  - We study spaces on manifolds with double weights and iterated discrete and continuous asymptotics, and their relationship with corner pseudo-differential operators.
KW  - manifolds with corners
KW  - iterated asymptotics
KW  - operators with corner symbols
KW  - 35J70
KW  - 47G30
KW  - 58J40
Y1  - 2014
U6  - https://doi.org/10.1080/17476933.2013.876416
SN  - 1747-6933
SN  - 1747-6941
VL  - 59
IS  - 12
SP  - 1706
EP  - 1738
PB  - Routledge, Taylor & Francis Group
CY  - Abingdon
ER  - 
TY  - JOUR
A1  - Chang, Der-Chen
A1  - Habal, Nadia
A1  - Schulze, Bert-Wolfgang
T1  - The edge algebra structure of the Zaremba problem
JF  - Journal of pseudo-differential operators and applications
N2  - We study mixed boundary value problems, here mainly of Zaremba type for the Laplacian within an edge algebra of boundary value problems. The edge here is the interface of the jump from the Dirichlet to the Neumann condition. In contrast to earlier descriptions of mixed problems within such an edge calculus, cf. (Harutjunjan and Schulze, Elliptic mixed, transmission and singular crack problems, 2008), we focus on new Mellin edge quantisations of the Dirichlet-to-Neumann operator on the Neumann side of the boundary and employ a pseudo-differential calculus of corresponding boundary value problems without the transmission property at the interface. This allows us to construct parametrices for the original mixed problem in a new and transparent way.
Y1  - 2014
U6  - https://doi.org/10.1007/s11868-013-0088-7
SN  - 1662-9981
SN  - 1662-999X
VL  - 5
IS  - 1
SP  - 69
EP  - 155
PB  - Springer
CY  - Basel
ER  - 
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  - https://doi.org/10.1007/s11785-013-0289-3
SN  - 1661-8254
SN  - 1661-8262
VL  - 8
IS  - 4
SP  - 803
EP  - 841
PB  - Springer
CY  - Basel
ER  - 
TY  - JOUR
A1  - Rungrottheera, Wannarut
A1  - Schulze, Bert-Wolfgang
A1  - Wong, M. W.
T1  - Iterative properties of pseudo-differential operators on edge spaces
JF  - Journal of pseudo-differential operators and applications
N2  - Pseudo-differential operators with twisted symbolic estimates play a large role in the calculus on manifolds with edge singularities. We study here aspects of the underlying abstract concept and establish a new result on iteration of quantizations.
KW  - Pseudo-differential operators
KW  - Twisted symbolic estimates
KW  - Quantizations
Y1  - 2014
U6  - https://doi.org/10.1007/s11868-014-0100-x
SN  - 1662-9981
SN  - 1662-999X
VL  - 5
IS  - 4
SP  - 455
EP  - 479
PB  - Springer
CY  - Basel
ER  -