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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

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