TY  - BOOK
A1  - Calvo, D.
A1  - Schulze, Bert-Wolfgang
T1  - Operators on Corner Manifolds with Exit to Infinity
T3  - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell
Y1  - 2005
SN  - 1437-739X
PB  - Univ.
CY  - Potsdam
ER  - 
TY  - INPR
A1  - Calvo, D.
A1  - Schulze, Bert-Wolfgang
T1  - Operators on corner manifolds with exit to infinity
N2  - We study (pseudo-)differential operators on a manifold with edge Z, locally modelled on a wedge with model cone that has itself a base manifold W with smooth edge Y . The typical operators A are corner degenerate in a specific way. They are described (modulo ‘lower order terms’) by a principal symbolic hierarchy σ(A) = (σ ψ(A), σ ^(A), σ ^(A)), where σ ψ is the interior symbol and σ ^(A)(y, η), (y, η) 2 T*Y \ 0, the (operator-valued) edge symbol of ‘first generation’, cf. [15]. The novelty here is the edge symbol σ^ of ‘second generation’, parametrised by (z, Ϛ) 2 T*Z \ 0, acting on weighted Sobolev spaces on the infinite cone with base W. Since such a cone has edges with exit to infinity, the calculus has the problem to understand the behaviour of operators on a manifold of that kind. We show the continuity of corner-degenerate operators in weighted edge Sobolev spaces, and we investigate the ellipticity of edge symbols of second generation. Starting from parameter-dependent elliptic families of edge operators of first generation, we obtain the Fredholm property of higher edge symbols on the corresponding singular infinite model cone.
T3  - Preprint - (2005) 01 
KW  - Operators on manifolds with edge and conical exit to infinity
KW  - Sobolev spaces with double weights on singular cones
Y1  - 2005
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-29753
ER  - 
TY  - INPR
A1  - Calvo, D.
A1  - Schulze, Bert-Wolfgang
T1  - Edge symbolic structures of second generation
N2  - Operators on a manifold with (geometric) singularities are degenerate in a natural way. They have a principal symbolic structure with contributions from the different strata of the configuration. We study the calculus of such operators on the level of edge symbols of second generation, based on specific quantizations of the corner-degenerate interior symbols, and show that this structure is preserved under compositions.
T3  - Preprint - (2005) 18 
KW  - Operators on manifolds with second order singularities
KW  - edge quantizations
KW  - continuity in Sobolev spaces with double weights
Y1  - 2005
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-29940
ER  -