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  - Hedayat Mahmoudi, Mahdi
A1  - Schulze, Bert-Wolfgang
T1  - A new approach to the second order edge calculus
JF  - Journal of pseudo-differential operators and applications
N2  - We establish essential steps of an iterative approach to operator algebras, ellipticity and Fredholm property on stratified spaces with singularities of second order. We cover, in particular, corner-degenerate differential operators. Our constructions are focused on the case where no additional conditions of trace and potential type are posed, but this case works well and will be considered in a forthcoming paper as a conclusion of the present calculus.
KW  - Operators on singular manifolds
KW  - Mellin transform
KW  - Stratified spaces
KW  - Ellipticity and parametrices
Y1  - 2018
U6  - https://doi.org/10.1007/s11868-017-0191-2
SN  - 1662-9981
SN  - 1662-999X
VL  - 9
IS  - 2
SP  - 265
EP  - 300
PB  - Springer
CY  - Basel
ER  - 
TY  - JOUR
A1  - Chang, Der-Chen
A1  - Hedayat Mahmoudi, Mahdi
A1  - Schulze, Bert-Wolfgang
T1  - Singular degenerate operators
JF  - Applicable analysis : an international journal
N2  - We outline some simplified and more general method for constructing parametrices on higher singular spaces. We also outline basic ideas on operators on manifolds with conical or edge singularities.
KW  - Operators on singular cones
KW  - Mellin symbols with values in the edge calculus
KW  - parametrices of elliptic operators
Y1  - 2017
U6  - https://doi.org/10.1080/00036811.2017.1336546
SN  - 0003-6811
SN  - 1563-504X
VL  - 96
IS  - 14
SP  - 2434
EP  - 2456
PB  - Routledge, Taylor & Francis Group
CY  - Abingdon
ER  -