Global analytic hypoellipticity for a class of evolution operators on T1 x S3

[摘要] 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 x 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. (C) 2021 Elsevier Inc. All rights reserved.

[发布日期] 2021-09-25

[关键词] Evolution equation;Partial Fourier series;Three dimensional sphere;Global analytic hypoellipticity;Low order perturbations