(Semi-)global analytic hypoellipticity for a class of “sums of squares” which fail to be locally analytic hypoelliptic

Chinni, Gregorio

doi:10.1090/proc/14464

Cited by 3 publications

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“…We emphasize that in a global (or semiglobal) setting the operator P 1 may be analytic hypoelliptic, suggesting that analytic hypoellipticity might be a consequence of the spectral behavior of some operator. Concerning this we cite the following theorem by Chinni [17]:…”

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confidence: 99%

Analytic regularity for solutions to sums of squares: an assessment

Bove

Mughetti

2020

Complex Anal Synerg

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We present a brief survey on the state of the theory of the real analytic regularity (real analytic hypoellipticity) for the solutions to sums of squares of vector fields satisfying the Hörmander condition. Contents 1. Introduction: the C ∞ hypoellipticity 1 2. The real analytic case: a short history, examples and counterexamples 5 3. Geometry of the characteristic variety: stratifications and the Treves conjecture 10 3.1. The analytic stratification 11 3.2. The symplectic stratification 12 3.3. The Poisson stratification 13 4. Examples and counterexamples 15 4.1. Examples 16 4.2. Counterexamples 18 5. Open problems 28 5.1. The 2 dimensional case 28 5.2. The 3 dimensional case 30 5.3. The case of dimension n ≥ 3 33 References 34

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