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Uniqueness of the Kontsevich-Vishik trace
Author(s):
L.
Maniccia;
E.
Schrohe;
J.
Seiler
Journal:
Proc. Amer. Math. Soc.
136
(2008),
747-752.
MSC (2000):
Primary 58J40, 58J42, 35S05
Posted:
November 1, 2007
MathSciNet review:
2358517
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Abstract:
Let  be a closed manifold. We show that the Kontsevich-Vishik trace, which is defined on the set of all classical pseudodifferential operators on  , whose (complex) order is not an integer greater than or equal to  , is the unique functional which (i) is linear on its domain, (ii) has the trace property and (iii) coincides with the  -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.
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Additional Information:
L.
Maniccia
Affiliation:
Università di Bologna, Dipartimento di Matematica, Piazza di Porta S. Donato 5, 40127 Bologna, Italy
Email:
maniccia@dm.unibo.it
E.
Schrohe
Affiliation:
Leibniz Universität Hannover, Institut für Analysis, Welfengarten 1, 30167 Hannover, Germany
Email:
schrohe@math.uni-hannover.de
J.
Seiler
Affiliation:
Leibniz Universität Hannover, Institut für Angewandte Mathematik, Welfengarten 1, 30167 Hannover, Germany
Email:
seiler@ifam.uni-hannover.de
DOI:
10.1090/S0002-9939-07-09168-X
PII:
S 0002-9939(07)09168-X
Keywords:
Kontsevich-Vishik canonical trace,
pseudodifferential operators
Received by editor(s):
February 9, 2007
Posted:
November 1, 2007
Dedicated:
Dedicated to Boris V. Fedosov on the occasion of his 70th birthday
Communicated by:
Mikhail Shubin
Copyright of article:
Copyright
2007,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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