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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
stationary phase