TY  - INPR
A1  - Dines, Nicoleta
A1  - Liu, X.
A1  - Schulze, Bert-Wolfgang
T1  - Edge quantisation of elliptic operators
N2  - The ellipticity of operators on a manifold with edge is defined as the bijectivity of the components of a principal symbolic hierarchy σ = (σψ, σ∧), where the second component takes value in operators on the infinite model cone of the local wedges. In general understanding of edge problems there are two basic aspects: Quantisation of edge-degenerate operators in weighted Sobolev spaces, and verifying the elliptcity of the principal edge symbol σ∧ which includes the (in general not explicitly known) number of additional conditions on the edge of trace and potential type. We focus here on these queations and give explicit answers for a wide class of elliptic operators that are connected with the ellipticity of edge boundary value problems and reductions to the boundary. In particular, we study the edge quantisation and ellipticity for Dirichlet-Neumann operators with respect to interfaces of some codimension on a boundary. We show analogues of the Agranovich-Dynin formula for edge boundary value problems, and we establish relations of elliptic operators for different weights, via the spectral flow of the underlying conormal symbols.
T3  - Preprint - (2004) 24 
KW  - Boundary value problems
KW  - edge singularities
KW  - ellipticity
KW  - spectral flow
Y1  - 2004
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-26838
ER  - 
TY  - INPR
A1  - Nazaikinskii, Vladimir
A1  - Savin, Anton
A1  - Schulze, Bert-Wolfgang
A1  - Sternin, Boris
T1  - Elliptic theory on manifolds with nonisolated singularities : III. The spectral flow of families of conormal symbols
N2  - When studyind elliptic operators on manifolds with nonisolated singularities one naturally encounters families of conormal symbols (i.e. operators elliptic with parameter p ∈ IR in the sense of Agranovich-Vishik) parametrized by the set of singular points. For homotopies of such families we define the notion of spectral flow, which in this case is an element of the K-group of the parameter space. We prove that the spectral flow is equal to the index of some family of operators on the infinite cone.
T3  - Preprint - (2002) 20 
KW  - elliptic family
KW  - conormal symbol
KW  - spectral flow
KW  - relative index
Y1  - 2002
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-26386
ER  - 
TY  - INPR
A1  - Savin, Anton
A1  - Sternin, Boris
T1  - Eta invariant and parity conditions
N2  - We give a formula for the η-invariant of odd order operators on even-dimensional manifolds, and for even order operators on odd-dimensional manifolds. Geometric second order operators are found with nontrivial η-invariants. This solves a problem posed by P. Gilkey.
T3  - Preprint - (2000) 21 
KW  - eta invariant
KW  - parity conditions
KW  - K-theory
KW  - linking coefficients
KW  - Dirac operators
KW  - spectral flow
KW  - elliptic operators
Y1  - 2000
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-25869
ER  -