an:01329205
Zbl 0932.35046
Bergamasco, Adalberto P.
Remarks about global analytic hypoellipticity
EN
Trans. Am. Math. Soc. 351, No. 10, 4113-4126 (1999).
00059977
1999
j
35H10
exponential Liouville numbers; exponential Liouville vectors; steepest descent; involutive systems; continued fractions
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.
P.Popivanov (Sofia)