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  - Hedayat Mahmoudi, Mahdi
A1  - Schulze, Bert-Wolfgang
T1  - Corner boundary value problems
JF  - Asian-European journal of mathematics
N2  - The paper develops some crucial steps in extending the first-order cone or edge calculus to higher singularity orders. We focus here on order 2, but the ideas are motivated by an iterative approach for higher singularities.
KW  - Mellin operators
KW  - Mellin oscillatory integrals
KW  - exit calculus
KW  - weighted Sobolev spaces
Y1  - 2016
U6  - https://doi.org/10.1142/S1793557117500541
SN  - 1793-5571
SN  - 1793-7183
VL  - 10
IS  - 1
PB  - World Scientific
CY  - Singapore
ER  - 
TY  - JOUR
A1  - Flad, H. -J.
A1  - Harutyunyan, Gohar
A1  - Schulze, Bert-Wolfgang
T1  - Asymptotic parametrices of elliptic edge operators
JF  - Journal of pseudo-differential operators and applications
N2  - We study operators on singular manifolds, here of conical or edge type, and develop a new general approach of representing asymptotics of solutions to elliptic equations close to the singularities. We introduce asymptotic parametrices, using tools from cone and edge pseudo-differential algebras. Our structures are motivated by models of many-particle physics with singular Coulomb potentials that contribute higher order singularities in Euclidean space, determined by the number of particles.
KW  - Cone and edge pseudo-differential operators
KW  - Ellipticity of edge-degenerate operators
KW  - Meromorphic operator-valued symbols
KW  - Asymptotics of solutions
Y1  - 2016
U6  - https://doi.org/10.1007/s11868-016-0159-7
SN  - 1662-9981
SN  - 1662-999X
VL  - 7
SP  - 321
EP  - 363
PB  - Springer
CY  - Basel
ER  - 
TY  - JOUR
A1  - Chang, D. -C.
A1  - Viahmoudi, M. Hedayat
A1  - Schulze, Bert-Wolfgang
T1  - PSEUDO-DIFFERENTIAL ANALYSIS WITH TWISTED SYMBOLIC STRUCTURE
JF  - Journal of nonlinear and convex analysis : an international journal
N2  - This paper is devoted to pseudo-differential operators and new applications. We establish necessary extensions of the standard calculus to specific classes of operator-valued symbols occurring in principal symbolic hierarchies of operators on manifolds with singularities or stratified spaces.
KW  - Pseudo-differential operators
KW  - boundary value problems
KW  - operator valued symbols
KW  - Fourier transform
Y1  - 2016
SN  - 1345-4773
SN  - 1880-5221
VL  - 17
SP  - 1889
EP  - 1937
PB  - Yokohama Publishers
CY  - Yokohama
ER  -