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# Ellipticity and Invertibility in the Cone Algebra on L P -sobolev Spaces

@inproceedings{SchroheEllipticityAI, title={Ellipticity and Invertibility in the Cone Algebra on L P -sobolev Spaces}, author={Elmar Schrohe and Jj Org Seiler} }

Given a manifold B with conical singularities, we consider the cone algebra with discrete asymptotics, introduced by Schulze, on a suitable scale of Lp-Sobolev spaces. Ellipticity is proven to be equivalent to the Fredholm property in these spaces; it turns out to be independent of the choice of p. We then show that the cone algebra is closed under inversion: whenever an operator is invertible between the associated Sobolev spaces, its inverse belongs to the calculus. We use these results to… CONTINUE READING