Entire and Meromorphic Functions in Several Complex Variables

摘要 宝琴 李 李将研究必要和充分的几何条件的分析品种是一个插值品种的加权 全函数空间在第二个方向，他将使用结果和方法的插值研究指数多项式 并得到Lojasiewicz型不等式，它们与一些 复分析和调和分析中的重要原理。 在第三个方向，他计划找到估计的体积零品种的整个全纯映射，这是密切相关的几何方面的插值品种。他还将学习 运动目标的“精炼”Nevanlinna第二基本定理， 特别注意亚纯函数的唯一性问题 函数和亚纯解（偏）微分方程。 许多重要的问题，如找到所有分布解决方案（或 找出是否有任何）的卷积方程系统 在信号处理、图像压缩和其他 应用可以转化为具有增长条件的整个函数的插值问题。 主题本身是几个复杂的主要问题之一， 变量拟议的研究的目标是丰富和推进上述领域的几个复变量及其 应用.

ABSTRACT Bao Qin Li Li will study necessary and sufficient geometric conditions for an analytic variety to be an interpolating variety for weighted spaces of entire functions. In a second direction, he will use results and methods of interpolation to study exponential polynomials and obtain Lojasiewicz type inequalities, which are tied to some important conjectures in complex and harmonic analysis. In a third direction, he plans to find estimates on the volume of zero varieties for entire holomorphic maps, which are closely related to geometric aspects of interpolating varieties. He will also study the "refined" Nevanlinna second fundamental theorem for moving targets, with special attention given to uniqueness problems of meromorphic functions and meromorphic solutions of (partial) differential equations. Many important problems like finding all distribution solutions (or finding out whether there are any) to systems of convolution equations arising in signal processing, image compression, and other applications can be translated to interpolation problems for entire functions with growth conditions. The topic itself is one of the major problems in several complex variables. The proposed research has as its goal to enrich and advance the above areas in several complex variables and their applications.