# 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.
19 Citations

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## References

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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

### Analytic hypo-ellipticity of a class of pseudodifferential operators with double characteristics and applications to the -neumann problem

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that is, if u must be a C ~ function in every open set where Pu is a C ~ function. Necessary and sufficient conditions for P to be hypoelliptic have been known for quite some time when the

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In this paper, we give some sufficient conditions for which the differential operatorP(λ=P0+λP1+...+λm−1Pm−1+λm, depending polynomially on the complex parameter λ, verifies the following statement:

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• 1992
Consider the hypersurface {(Z1, Z2): Q(Z2) = P(zi)} cC C2, where P : R is a subharmonic, nonharmonic polynomial. Such a surface is pseudoconvex (more precisely, is the boundary of a pseudoconvex

### The analysis of linear partial differential operators

the analysis of linear partial differential operators i distribution theory and fourier rep are a good way to achieve details about operating certainproducts. Many products that you buy can be

### Sur un problème aux valeurs propres non linéaire

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