Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Uniqueness of the Kontsevich-Vishik trace

Authors: L. Maniccia, E. Schrohe and J. Seiler
Journal: Proc. Amer. Math. Soc. 136 (2008), 747-752
MSC (2000): Primary 58J40, 58J42, 35S05
Published electronically: November 1, 2007
MathSciNet review: 2358517
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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 $ L^2$-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

E. Schrohe
Affiliation: Leibniz Universität Hannover, Institut für Analysis, Welfengarten 1, 30167 Hannover, Germany

J. Seiler
Affiliation: Leibniz Universität Hannover, Institut für Angewandte Mathematik, Welfengarten 1, 30167 Hannover, Germany

Keywords: Kontsevich-Vishik canonical trace, pseudodifferential operators
Received by editor(s): February 9, 2007
Published electronically: November 1, 2007
Dedicated: Dedicated to Boris V. Fedosov on the occasion of his 70th birthday
Communicated by: Mikhail Shubin
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.