Analytic hypoellipticity in dimension two

1996/02/04 by Michael Christ, Christ, Michael
Mathematics · #Algebraic and Geometric Analysis #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Mathematical Analysis and Transform Methods

paper · pdf · doi:10.48550/arxiv.math/9602209

openalex publication_date 1996/02/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A simple geometric condition is sufficient for analytic hypoellipticity of sums of squares of two vector fields in \mathbb R². This condition is proved to be necessary for generic vector fields and for various special cases, and to be both necessary and sufficient for a closely related family of operators.

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