Details
| Original language | English |
|---|---|
| Pages (from-to) | 403-425 |
| Number of pages | 23 |
| Journal | Annals of Global Analysis and Geometry |
| Volume | 14 |
| Issue number | 4 |
| Publication status | Published - Nov 1996 |
| Externally published | Yes |
Abstract
Let B be a manifold with conical singularities, and denote by the smooth bounded manifold with cylindrical ends obtained by blowing up near the singularities. B.-W. Schulze has developed a framework for a pseudodifferential calculus on B by defining various classes of distribution spaces and operator algebras, working in fixed coordinates on the manifold. I am showing here that the Mellin Sobolev spaces without asymptotics, the cone algebra without asymptotics, and its ideal of smoothing operators are independent of the choice of coordinates and therefore may be considered intrinsic objects for manifolds with conical singularities.
Keywords
- Manifolds with conical singularities, Mellin calculus, Pseudodifferential operators
ASJC Scopus subject areas
- Mathematics(all)
- Analysis
- Social Sciences(all)
- Political Science and International Relations
- Mathematics(all)
- Geometry and Topology
Cite this
- Standard
- Harvard
- Apa
- Vancouver
- BibTeX
- RIS
In: Annals of Global Analysis and Geometry, Vol. 14, No. 4, 11.1996, p. 403-425.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Invariance of the cone algebra without asymptotics
AU - Schrohe, Elmar
N1 - Copyright: Copyright 2018 Elsevier B.V., All rights reserved.
PY - 1996/11
Y1 - 1996/11
N2 - Let B be a manifold with conical singularities, and denote by the smooth bounded manifold with cylindrical ends obtained by blowing up near the singularities. B.-W. Schulze has developed a framework for a pseudodifferential calculus on B by defining various classes of distribution spaces and operator algebras, working in fixed coordinates on the manifold. I am showing here that the Mellin Sobolev spaces without asymptotics, the cone algebra without asymptotics, and its ideal of smoothing operators are independent of the choice of coordinates and therefore may be considered intrinsic objects for manifolds with conical singularities.
AB - Let B be a manifold with conical singularities, and denote by the smooth bounded manifold with cylindrical ends obtained by blowing up near the singularities. B.-W. Schulze has developed a framework for a pseudodifferential calculus on B by defining various classes of distribution spaces and operator algebras, working in fixed coordinates on the manifold. I am showing here that the Mellin Sobolev spaces without asymptotics, the cone algebra without asymptotics, and its ideal of smoothing operators are independent of the choice of coordinates and therefore may be considered intrinsic objects for manifolds with conical singularities.
KW - Manifolds with conical singularities
KW - Mellin calculus
KW - Pseudodifferential operators
UR - http://www.scopus.com/inward/record.url?scp=26444596192&partnerID=8YFLogxK
U2 - 10.1007/BF00129899
DO - 10.1007/BF00129899
M3 - Article
AN - SCOPUS:26444596192
VL - 14
SP - 403
EP - 425
JO - Annals of Global Analysis and Geometry
JF - Annals of Global Analysis and Geometry
SN - 0232-704X
IS - 4
ER -