## Uniqueness of the Kontsevich-Vishik trace

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- by L. Maniccia, E. Schrohe and J. Seiler PDF
- Proc. Amer. Math. Soc.
**136**(2008), 747-752 Request permission

## 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.## References

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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
- Received by editor(s): February 9, 2007
- Published electronically: November 1, 2007
- Communicated by: Mikhail Shubin
- © Copyright 2007
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc.
**136**(2008), 747-752 - MSC (2000): Primary 58J40, 58J42, 35S05
- DOI: https://doi.org/10.1090/S0002-9939-07-09168-X
- MathSciNet review: 2358517

Dedicated: Dedicated to Boris V. Fedosov on the occasion of his 70th birthday