论文标题
伪差异操作员的一类超确定系统的全球性低纤维化性
Global hypoellipticity for a class of overdetermined systems of pseudo-differential operators on the torus
论文作者
论文摘要
本文研究了在圆环上定义的伪差异操作员的一类过度确定系统的全球性低纤维化。主要目标是建立系统的全球性低纤维化与其正常形式的全球性低纤维化之间的联系。事实证明，数量理论性质的阻塞似乎是全球性低下的必要条件。相反，足以接近三种类型的假设：Hörmander条件，对数增长和超同源性生长。
This article studies the global hypoellipticity of a class of overdetermined systems of pseudo-differential operators defined on the torus. The main goal consists in establishing connections between the global hypoellipticity of the system and the global hypoellipticity of its normal form. It is proved that an obstruction of number-theoretical nature appears as a necessary condition to the global hypoellipticity. Conversely, the sufficiency is approached ana\-lyzing three types of hypotheses: a Hörmander condition, logarithmic growth and super-logarithmic growth.
