# 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
43 Citations
The proof of the Nirenberg-Treves conjecture
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