Harmonic Analysis and Complex Non-linear PDEs with Applications

摘要 李松英 李先生正在研究谐波分析中的几个问题， 分析和非线性偏微分方程。他的项目 包括电晕问题在几个复杂的变量。李将 考虑Hankel算子、复算子、复合算子和复Monge-Ampere算子。李正专注于存在， 复Monge-Ampere方程解的唯一性和正则性 光滑有界弱伪凸域上的微分方程这些 结果可直接应用于边界行为的研究 Kahler-Einstein metrics的缩写。 李的项目旨在发展理论和 调和分析、复分析和偏微分方程的应用 微分方程该项目的理论部分是 关注这些领域的几个重要问题。 该项目的主要问题与控制理论、数学物理、特别是 量子力学和近似理论。 系统控制理论可以 直接应用于电气和计算机工程 近似理论可以用来处理 信号处理

ABSTRACT Song-Ying Li Li is investigating several problems in harmonic analysis, complex analysis and non-linear partial differential equations. His project includes the Corona problem in several complex variables. Li will consider Hankel operators, commutators, composition operators and the complex Monge-Ampere operator. Li is focusing on the existence, uniqueness and regularity of solutions of complex Monge-Ampere equations on smoothly bounded weakly pseudoconvex domains. These results can be directly applied to the study of the boundary behavior of Kahler-Einstein metrics. The project of Li is aimed at developing both the theory and application of harmonic analysis, complex analysis and partial differential equations. The theoretical part of the project is concerned with several important problems in these fields. The main problems of this project are strongly related to control theory, mathematical physics, especially quantum mechanics and approximation theory. The theory of systems control can be directly applied to Electrical and Computer Engineering and approximation theory can be used to deal with problems in signal processing.