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  - INPR
A1  - Nazaikinskii, Vladimir
A1  - Schulze, Bert-Wolfgang
A1  - Sternin, Boris
A1  - Shatalov, Victor
T1  - Quantization of symplectic transformations on manifolds with conical singularities
N2  - The structure of symplectic (canonical) transformations on manifolds with conical singularities is established. The operators associated with these transformations are defined in the weight spaces and their properties investigated.
T3  - Preprint - (1997) 23 
KW  - manifolds with conical singularities
KW  - symplectic (canonical) transformations
KW  - quantization
KW  - Mellin transform
Y1  - 1997
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-25084
ER  - 
TY  - INPR
A1  - Schulze, Bert-Wolfgang
A1  - Sternin, Boris
A1  - Shatalov, Victor
T1  - On the index of differential operators on manifolds with conical singularities
N2  - The paper contains the proof of the index formula for manifolds with conical points. For operators subject to an additional condition of spectral symmetry, the index is expressed as the sum of multiplicities of spectral points of the conormal symbol (indicial family) and the integral from the Atiyah-Singer form over the smooth part of the manifold. The obtained formula is illustrated by the example of the Euler operator on a two-dimensional manifold with conical singular point.
T3  - Preprint - (1997) 10 
KW  - conical singularities
KW  - Mellin transform
KW  - pseudodiferential operators
KW  - ellipticity
KW  - Fredholm operators
KW  - regularizers
KW  - analytic index
Y1  - 1997
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-24965
ER  -