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Global analytic hypoellipticity and pseudoperiodic functions. (English) Zbl 0979.35036
Summary: We show that a class of overdetermined systems on the 3-torus associated to a closed 1-form \(c\) on the 2-torus \(\mathbb{T}^2\simeq \mathbb{R}^2/2\pi\mathbb{Z}^2\) is globally analytic hypoelliptic if and only if every \(B:\mathbb{R}^2\to\mathbb{R}\) such that \(dB=\operatorname{Im} c\) is an open map at each point.

MSC:
35H10 Hypoelliptic equations
35N05 Overdetermined systems of PDEs with constant coefficients
35F05 Linear first-order PDEs
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