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Remarks about global analytic hypoellipticity. (English) Zbl 0932.35046
In the paper under consideration a necessary and sufficient condition for the global analytic hypoellipticity (GAH) on the torus \(T^2\) of the first-order operator \(L= \partial_t+ (a(t)+ ib(t))\partial_x\) is proved. The coefficients \(a\), \(b\) of \(L\) are real-valued, real-analytic functions on the unit circle.
In Section 3 a necessary and sufficient condition for GAH of the involutive system of vector fields \(L_j= \partial_j+ c_j(t_j)\partial_x\), \(j= 1,\dots, n\) on \(T^{n+1}\) is shown. The author proposes several examples illustrating his main results.

MSC:
35H10 Hypoelliptic equations
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