Details
| Original language | English |
|---|---|
| Pages (from-to) | 93-114 |
| Number of pages | 22 |
| Journal | Integral Equations and Operator Theory |
| Volume | 41 |
| Issue number | 1 |
| Publication status | Published - Mar 2001 |
| Externally published | Yes |
Abstract
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 analyze the behaviour of these operators on Lp(B).
ASJC Scopus subject areas
- Mathematics(all)
- Analysis
- Mathematics(all)
- Algebra and Number Theory
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In: Integral Equations and Operator Theory, Vol. 41, No. 1, 03.2001, p. 93-114.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Ellipticity and invertibility in the cone algebra on Lp-Sobolev spaces
AU - Schrohe, Elmar
AU - Seiler, Jörg
N1 - Copyright: Copyright 2005 Elsevier B.V., All rights reserved.
PY - 2001/3
Y1 - 2001/3
N2 - 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 analyze the behaviour of these operators on Lp(B).
AB - 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 analyze the behaviour of these operators on Lp(B).
UR - http://www.scopus.com/inward/record.url?scp=0038101966&partnerID=8YFLogxK
U2 - 10.1007/BF01202533
DO - 10.1007/BF01202533
M3 - Article
AN - SCOPUS:0038101966
VL - 41
SP - 93
EP - 114
JO - Integral Equations and Operator Theory
JF - Integral Equations and Operator Theory
SN - 0378-620X
IS - 1
ER -