TY  - JOUR
A1  - Chang, Der-Chen
A1  - Schulze, Bert-Wolfgang
T1  - Ellipticity on spaces with higher singularities
JF  - Science China Mathematics
N2  - We study corner-degenerate pseudo-differential operators of any singularity order and develop ellipticity based on the principal symbolic hierarchy, associated with the stratification of the underlying space. We construct parametrices within the calculus and discuss the aspect of additional trace and potential conditions along lower-dimensional strata.
KW  - pseudo-differential operators
KW  - operator-valued symbols
KW  - Fourier and Mellin transforms
Y1  - 2017
U6  - https://doi.org/10.1007/s11425-016-0519-9
SN  - 1674-7283
SN  - 1869-1862
VL  - 60
IS  - 11
SP  - 2053
EP  - 2076
PB  - Science China Press
CY  - Beijing
ER  - 
TY  - JOUR
A1  - Chang, Der-Chen
A1  - Schulze, Bert-Wolfgang
T1  - Corner spaces and Mellin quantization
JF  - Journal of nonlinear and convex analysis : an international journal
N2  - Manifolds with corners in the present investigation are non-smooth configurations - specific stratified spaces - with an incomplete metric such as cones, manifolds with edges, or corners of piecewise smooth domains in Euclidean space. We focus here on operators on such "corner manifolds" of singularity order <= 2, acting in weighted corner Sobolev spaces. The corresponding corner degenerate pseudo-differential operators are formulated via Mellin quantizations, and they also make sense on infinite singular cones.
KW  - Mellin quantizations
KW  - operator-valued symbols
KW  - weighted edge and corner spaces
Y1  - 2018
SN  - 1345-4773
SN  - 1880-5221
VL  - 19
IS  - 2
SP  - 179
EP  - 195
PB  - Yokohama Publishers
CY  - Yokohama
ER  -