arXiv math/05041592005-04-07math.APmath.CVmath.SG

Analytic Hypoellipticity for a Class of Sums of Squares of Vector Fields with Non-Symplectic Characteristic Variety

Antonio Bove, Makhlouf Derridj, David S. Tartakoff

备注：: 11 pages
发表信息：: Journal of Functional Analysis {\bf 234} (2), (2006), pp~464-472.

英文摘要：

The recent example of Hanges: $P = \partial_t^2 + t^2Δ_x + \partial^2_{θ(x)}$ in $R^3$ is analytic hypoelliptic in the sense of germs but not in the strong sense in any neighborhood of the origin. And its characteristic variety is non-symplectic. We give a purely $L^2,$ and hence quite flexible, proof of this result and generalizations, and link it to, and contrast it with, the celebrated Baouendi-Goulaouic operator. We point out that the results are consistent with the conjecture of Treves.

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