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Proceedings of the American Mathematical Society

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

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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.
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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

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