Some non-analytic-hypoelliptic sums of squares of vector fields

@article{Christ1992SomeNS,
  title={Some non-analytic-hypoelliptic sums of squares of vector fields},
  author={Michael Christ},
  journal={Bulletin of the American Mathematical Society},
  year={1992},
  volume={26},
  pages={137-140}
}
  • M. Christ
  • Published 1 January 1992
  • Mathematics
  • Bulletin of the American Mathematical Society
Certain second-order partial differential operators, which are expressed as sums of squares of real-analytic vector fields in $\Bbb R^3$ and which are well known to be $C^\infty$ hypoelliptic, fail to be analytic hypoelliptic. 

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Certain sums of Squares of Vector Fields Fail to be Analytic Hypoelliptic

If m {3,4,5,...} then the partial differential operator in R3 fails to be analytic hypoelliptic. This results from the existence of parameters C such that the ordinary differential equation has a

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