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Global $$s$$-solvability, global $$s$$-hypoellipticity and Diophantine phenomena. (English) Zbl 1065.35100
Summary: We consider the problem of global Gevrey solvability for a class of sub-Laplacians on a torus with coefficients in the Gevrey class $$G^s(\mathbb T^N)$$. For this class of operators we show that global Gevrey solvability and global Gevrey hypoellipticity are both equivalent to the condition that the coefficients satisfy a Diophantine condition.

##### MSC:
 35H10 Hypoelliptic equations 35C10 Series solutions to PDEs 35A05 General existence and uniqueness theorems (PDE) (MSC2000) 35H20 Subelliptic equations
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