The resolution of the Nirenberg-Treves conjecture

@article{Dencker2003TheRO,
  title={The resolution of the Nirenberg-Treves conjecture},
  author={Nils Dencker},
  journal={Annals of Mathematics},
  year={2003},
  volume={163},
  pages={405-444}
}
  • N. Dencker
  • Published 2003
  • Mathematics
  • Annals of Mathematics
We give a proof of the Nirenberg-Treves conjecture: that local solvability of principal-type pseudo-differential operators is equivalent to condition (Psi). This condition rules out sign changes from - to + of the imaginary part of the principal symbol along the oriented bicharacteristics of the real part. We obtain local solvability by proving a localizable a priori estimate for the adjoint operator with a loss of two derivatives (compared with the elliptic case). The proof involves a new… Expand
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