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Traces on pseudodifferential operators and sums of commutators

Abstract

The aim of this paper is to show that various known characterizations of traces on classical pseudodifferential operators can actually be obtained by very elementary considerations on pseudodifferential operators, using only basic properties of these operators. Thereby, we give a unified treatment of the determinations of the space of traces (i) on ΨDOs of non-integer order or of regular parity-class, (ii) on integer order ΨDOs, (iii) on ΨDOs of non-positive orders in dimension ≥ 2, and (iv) on ΨDOs of non-positive orders in dimension 1.

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Author information

Correspondence to Raphaël Ponge.

Additional information

Research partially supported by NSERC grant 341328-07 and by a New Staff Matching grant from the Connaught Fund of the University of Toronto

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Ponge, R. Traces on pseudodifferential operators and sums of commutators. JAMA 110, 1–30 (2010). https://doi.org/10.1007/s11854-010-0001-8

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Keywords

  • Steklov Institute
  • PSEUDODIFFERENTIAL Operator
  • Principal Symbol
  • Local Chart
  • Smoothing Operator