TY  - JOUR
A1  - Lyu, Xiaojing
A1  - Qian, Tao
A1  - Schulze, Bert-Wolfgang
T1  - Order filtrations of the edge algebra
JF  - Journal of pseudo-differential operators and applications
N2  - By edge algebra we understand a pseudo-differential calculus on a manifold with edge. The operators have a two-component principal symbolic hierarchy which determines operators up to lower order terms. Those belong to a filtration of the corresponding operator spaces. We give a new characterisation of this structure, based on an alternative representation of edge amplitude functions only containing holomorphic edge-degenerate Mellin symbols.
Y1  - 2015
U6  - https://doi.org/10.1007/s11868-015-0126-8
SN  - 1662-9981
SN  - 1662-999X
VL  - 6
IS  - 3
SP  - 279
EP  - 305
PB  - Springer
CY  - Basel
ER  - 
TY  - THES
A1  - Lyu, Xiaojing
T1  - Operators on singular manifolds
T1  - Operatoren auf singuläre Mannigfaltigkeiten
N2  - We study the interplay between analysis on manifolds with singularities and complex analysis and develop new structures of operators based on the Mellin transform and tools for iterating the calculus for higher singularities. We refer to the idea of interpreting boundary value problems (BVPs) in terms of pseudo-differential operators with a principal symbolic hierarchy, taking into account that BVPs are a source of cone and edge operator algebras. The respective cone and edge pseudo-differential algebras in turn are the starting point of higher corner theories. In addition there are deep relationships between corner operators and complex analysis. This will be illustrated by the Mellin symbolic calculus.
N2  - Wir studieren den Zusammenhang zwischen Analysis auf Mannigfaltigkeiten mit Singularitäten und komplexer Analysis und entwickeln neue Strukturen von Operatoren basierend auf der Mellin-Transformation und Hilfsmitteln für die Iteration des Kalküls für höhere Singularitäten. Wir beziehen uns auf die Idee von der Interpretation von Randwert-Problemen (BVPs) durch Pseudo-Differential-operatoren und Hauptsymbol-Hierarchien, unter Berüksichtigung der Tatsache, dass BVPs eine Quelle von Konus- und Kanten-Operator- algebren sind. Die betreffenden Konus- und Kanten-Pseudo-differentiellen Algebren sind wiederum der Startpunkt von höheren Eckentheorien. Zusätzlich bestehen tiefe Beziehungen zwischen Ecken-Operatoren und komplexer Analysis. Dies wird illustiert durch den Mellin-Symbol Kalkül.
KW  - order filtration
KW  - Mellin-Symbols
KW  - singular manifolds
KW  - Ordnungs-Filtrierung
KW  - Mellin-Symbole
KW  - singuläre Mannigfaltigkeiten
Y1  - 2016
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-103643
ER  - 
TY  - JOUR
A1  - Lyu, Xiaojing
A1  - Schulze, Bert-Wolfgang
T1  - Mellin Operators in the Edge Calculus
JF  - Complex analysis and operator theory
N2  - A manifold M with smooth edge Y is locally near Y modelled on X-Delta x Omega for a cone X-Delta := ( (R) over bar (+) x X)/({0} x X) where Xis a smooth manifold and Omega subset of R-q an open set corresponding to a chart on Y. Compared with pseudo-differential algebras, based on other quantizations of edge-degenerate symbols, we extend the approach with Mellin representations on the r half-axis up to r = infinity, the conical exit of X-boolean AND = R+ x X (sic) (r, x) at infinity. The alternative description of the edge calculus is useful for pseudo-differential structures on manifolds with higher singularities.
KW  - Edge degenerate operators
KW  - Mellin and Green operators edge symbols
Y1  - 2016
U6  - https://doi.org/10.1007/s11785-015-0511-6
SN  - 1661-8254
SN  - 1661-8262
VL  - 10
SP  - 965
EP  - 1000
PB  - Springer
CY  - Basel
ER  - 
TY  - JOUR
A1  - Rungrottheera, Wannarut
A1  - Lyu, Xiaojing
A1  - Schulze, Bert-Wolfgang
T1  - Parameter-dependent edge calculus and corner parametrices
JF  - Journal of nonlinear and convex analysis : an international journal
N2  - Let B be a compact manifold with smooth edge of dimension > 0. We study the interplay between parameter-dependent edge algebra algebra on B and operator families belonging to the corner calculus, and we characterize parametrices in the corner case.
KW  - Edge calculus
KW  - corner parametrices
Y1  - 2018
SN  - 1345-4773
SN  - 1880-5221
VL  - 19
IS  - 12
SP  - 2021
EP  - 2051
PB  - Yokohama Publishers
CY  - Yokohama
ER  -