TY  - INPR
A1  - Ma, L.
A1  - Schulze, Bert-Wolfgang
T1  - Operators on manifolds with conical singularities
N2  - We construct elliptic elements in the algebra of (classical pseudo-differential) operators on a manifold M with conical singularities. The ellipticity of any such operator A refers to a pair of principal symbols (σ0, σ1) where σ0 is the standard (degenerate) homogeneous principal symbol, and σ1 is the so-called conormal symbol, depending on the complex Mellin covariable z. The conormal symbol, responsible for the conical singularity, is operator-valued and acts in Sobolev spaces on the base X of the cone. The σ1-ellipticity is a bijectivity condition for all z of real part (n + 1)/2 − γ, n = dimX, for some weight γ. In general, we have to rule out a discrete set of exceptional weights that depends on A. We show that for every operator A which is elliptic with respect to σ0, and for any real weight γ there is a smoothing Mellin operator F in the cone algebra such that A + F is elliptic including σ1. Moreover, we apply the results to ellipticity and index of (operator-valued) edge symbols from the calculus on manifolds with edges.
T3  - Preprint - (2009) 07 
KW  - Operators on manifolds with conical singularities
KW  - conormal symbols
KW  - ellipticity of cone operators
Y1  - 2009
UR  - https://publishup.uni-potsdam.de/frontdoor/index/index/docId/3451
UR  - https://nbn-resolving.org/urn:nbn:de:kobv:517-opus-36608
ER  -