Global analytic hypoellipticity for a class of evolution operators on [formula omitted].

In this paper, we present necessary and sufficient conditions to have global analytic hypoellipticity for a class of first-order operators defined on T 1 × S 3. In the case of real-valued coefficients, we prove that an operator in this class is conjugated to a constant-coefficient operator satisfying a Diophantine condition, and that such conjugation preserves the global analytic hypoellipticity. In the case where the imaginary part of the coefficients is non-zero, we show that the operator is globally analytic hypoelliptic if the Nirenberg-Treves condition (P) holds, in addition to an analytic Diophantine condition. [ABSTRACT FROM AUTHOR]