Mathematical Sciences: Problems in Harmonic Analysis and Several Complex Variables

小行星9500758 李将调查几个问题在复杂的分析，包括电晕问题在几个复杂的变量;理论的功能空间，如哈代空间，伯格曼空间，和Lipschitz空间，域在复杂的欧几里德空间;和运营商理论的功能空间。 他还将研究复杂的非线性微分方程的边值问题。 多复变出现在世纪初作为一个自然的产物研究的职能，一个复杂的变量。 很明显，这个理论与它的前身有很大的不同。 基本的几何是更难以把握和函数理论有更多的亲和力与偏微分算子的一阶。 因此，它成长为一个混合学科结合了微分几何和微分方程的深刻特点。 许多基本结构是在过去三十年中确定的。 目前的研究仍然集中在理解这些基本的数学形式。

9500758 Li Li will investigate several problems in complex analysis, including the Corona problem in several complex variables; the theory of function spaces, such as Hardy spaces, Bergman spaces, and Lipschitz spaces, on domains in complex Euclidean space; and operator theory on function spaces. He will also study the boundary value problem of complex non-linear differential equations. Several complex variables arose at the beginning of the century as a natural outgrowth of studies of functions of one complex variable. It became clear early on that the theory differed widely from it predecessor. The underlying geometry was far more difficult to grasp and the function theory had far more affinity with partial differential operators of first order. It thus grew as a hybrid subject combining deep characteristics of differential geometry and differential equations. Many of the fundamental structures were defined in the last three decades. Current studies still concentrate on understanding these basic mathematical forms.