论文标题
$ \ mathbb {t}^1 \ times \ mathbb {s}^3 $ on $ \ mathbb {t}^1
Global analytic hypoellipticity for a class of evolution operators on $\mathbb{T}^1\times\mathbb{S}^3$
论文作者
论文摘要
在本文中，我们提出了必要和足够的条件，以使在$ \ mathbb {t}^1 \ times \ times \ mathbb {s}^3 $上定义的一类全局分析性低纤维化。在实价系数的情况下，我们证明该类别的运算符与满足双苯胺条件的恒定运算符相结合，并且这种共轭保留了全球分析性低纤维化性。在系数的虚构部分非零的情况下，我们表明操作员在全球性分析性低纤维中，如果Nirenberg-treves条件（$ \ MATHCAL {P} $）保持，除了二磷抗菌条件外。
In this paper, we present necessary and sufficient conditions to have global analytic hypoellipticity for a class of first-order operators defined on $\mathbb{T}^1 \times \mathbb{S}^3$. 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 ($\mathcal{P}$) holds, in addition to a Diophantine condition.
