We are concerned with the problem of the analytic hypoellipticity; precisely, we focus on the real analytic regularity of the solutions of sums of squares with real analytic coefficients. Treves conjecture states that an operator of this type is analytic hypoelliptic if and only if all the strata in the Poisson-Treves stratification are symplectic. We discuss a model operator, P, (firstly appeared and studied in [3]) having a single symplectic stratum and prove that it is not analytic hypoelliptic. This yields a counterexample to the sufficient part of Treves conjecture; the necessary part is still an open problem.

Mughetti, M. (2016). Analytic Hypoellipticity and the Treves Conjecture. BRUNO PINI MATHEMATICAL ANALYSIS SEMINAR, 1, 53-68 [10.6092/issn.2240-2829/6690].

Analytic Hypoellipticity and the Treves Conjecture

MUGHETTI, MARCO
2016

Abstract

We are concerned with the problem of the analytic hypoellipticity; precisely, we focus on the real analytic regularity of the solutions of sums of squares with real analytic coefficients. Treves conjecture states that an operator of this type is analytic hypoelliptic if and only if all the strata in the Poisson-Treves stratification are symplectic. We discuss a model operator, P, (firstly appeared and studied in [3]) having a single symplectic stratum and prove that it is not analytic hypoelliptic. This yields a counterexample to the sufficient part of Treves conjecture; the necessary part is still an open problem.
2016
Mughetti, M. (2016). Analytic Hypoellipticity and the Treves Conjecture. BRUNO PINI MATHEMATICAL ANALYSIS SEMINAR, 1, 53-68 [10.6092/issn.2240-2829/6690].
Mughetti, Marco
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11585/608983
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