论文标题
在复杂空间的平滑真实亚曼叶上的Denjoy-Carleman微局部规律性
Denjoy-Carleman Microlocal Regularity on Smooth Real Submanifolds of Complex Space
论文作者
论文摘要
我们证明了（常规）Denjoy-Carleman在某些光滑复杂矢量场的某些系统中证明了近似解决方案的存在。这样的近似解决方案提供了一个明确定义的Denjoy-Carleman波浪前组的概念，该概念是在复杂空间中最大真实的Submanifolds上的分布组集，可以根据傅立叶bros-iagolnitzer变换的衰减来表征。我们还采用了近似解决方案来分析某些一阶非线性偏微分方程某些系统解决方案的Denjoy-Carleman微局部规则性。
We prove the existence of approximate solutions in the (regular) Denjoy-Carleman sense for some systems of smooth complex vector fields. Such approximate solutions provide a well defined notion of Denjoy-Carleman wave front set of distributions on maximally real submanifolds in complex space which can be characterized in terms of the decay of the Fourier-Bros-Iagolnitzer transform. We also apply the approximate solutions to analyze the Denjoy-Carleman microlocal regularity of solutions of certain systems of first-order nonlinear partial differential equations.
