Details
| Original language | English |
|---|---|
| Pages (from-to) | 747-752 |
| Number of pages | 6 |
| Journal | Proceedings of the American Mathematical Society |
| Volume | 136 |
| Issue number | 2 |
| Publication status | Published - Feb 2008 |
Abstract
Let M be a closed manifold. We show that the Kontsevich-Vishik trace, which is defined on the set of all classical pseudodifferential operators on M, whose (complex) order is not an integer greater than or equal to - dim M, is the unique functional which (i) is linear on its domain, (ii) has the trace property and (iii) coincides with the L2-operator trace on trace class operators. Also the extension to even-even pseudodifferential operators of arbitrary integer order on odd-dimensional manifolds and to even-odd pseudodifferential operators of arbitrary integer order on even-dimensional manifolds is unique.
Keywords
- Kontsevich-vishik canonical trace, Pseudodifferential operators
ASJC Scopus subject areas
- Mathematics(all)
- General Mathematics
- Mathematics(all)
- Applied Mathematics
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In: Proceedings of the American Mathematical Society, Vol. 136, No. 2, 02.2008, p. 747-752.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Uniqueness of the kontsevich-vishik trace
AU - Maniccia, L.
AU - Schrohe, E.
AU - Seiler, J.
N1 - Copyright: Copyright 2010 Elsevier B.V., All rights reserved.
PY - 2008/2
Y1 - 2008/2
N2 - Let M be a closed manifold. We show that the Kontsevich-Vishik trace, which is defined on the set of all classical pseudodifferential operators on M, whose (complex) order is not an integer greater than or equal to - dim M, is the unique functional which (i) is linear on its domain, (ii) has the trace property and (iii) coincides with the L2-operator trace on trace class operators. Also the extension to even-even pseudodifferential operators of arbitrary integer order on odd-dimensional manifolds and to even-odd pseudodifferential operators of arbitrary integer order on even-dimensional manifolds is unique.
AB - Let M be a closed manifold. We show that the Kontsevich-Vishik trace, which is defined on the set of all classical pseudodifferential operators on M, whose (complex) order is not an integer greater than or equal to - dim M, is the unique functional which (i) is linear on its domain, (ii) has the trace property and (iii) coincides with the L2-operator trace on trace class operators. Also the extension to even-even pseudodifferential operators of arbitrary integer order on odd-dimensional manifolds and to even-odd pseudodifferential operators of arbitrary integer order on even-dimensional manifolds is unique.
KW - Kontsevich-vishik canonical trace
KW - Pseudodifferential operators
UR - http://www.scopus.com/inward/record.url?scp=77950626375&partnerID=8YFLogxK
U2 - 10.1090/S0002-9939-07-09168-X
DO - 10.1090/S0002-9939-07-09168-X
M3 - Article
AN - SCOPUS:77950626375
VL - 136
SP - 747
EP - 752
JO - Proceedings of the American Mathematical Society
JF - Proceedings of the American Mathematical Society
SN - 0002-9939
IS - 2
ER -