TY  - JOUR
A1  - Mahmoudi, Mahdi Hedayat
A1  - Schulze, Bert-Wolfgang
A1  - Tepoyan, Liparit
T1  - Continuous and variable branching asymptotics
JF  - Journal of pseudo-differential operators and applications
N2  - The regularity of solutions to elliptic equations on a manifold with singularities, say, an edge, can be formulated in terms of asymptotics in the distance variable r > 0 to the singularity. In simplest form such asymptotics turn to a meromorphic behaviour under applying the Mellin transform on the half-axis. Poles, multiplicity, and Laurent coefficients form a system of asymptotic data which depend on the specific operator. Moreover, these data may depend on the variable y along the edge. We then have y-dependent families of meromorphic functions with variable poles, jumping multiplicities and a discontinuous dependence of Laurent coefficients on y. We study here basic phenomena connected with such variable branching asymptotics, formulated in terms of variable continuous asymptotics with a y-wise discrete behaviour.
KW  - Asymptotics of solutions
KW  - Weighted edge spaces
KW  - Edge symbols
Y1  - 2015
U6  - https://doi.org/10.1007/s11868-015-0110-3
SN  - 1662-9981
SN  - 1662-999X
VL  - 6
IS  - 1
SP  - 69
EP  - 112
PB  - Springer
CY  - Basel
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  -