Entire and Meromorphic Functions in Several Complex Variables

多个复变量中的全函数和亚纯函数

• 批准号: 9706376
• 负责人: B L
• 金额: $ 6.02万
• 依托单位: Boston College
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1997
• 资助国家: 美国
• 起止时间: 1997-07-01 至 2000-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9706376&HistoricalAwards=false
• 关键词: Entire; Meromorphic; Functions; Several; Complex

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.

李莉（Bao Qin Li Li）将研究一个解析变量是整个函数加权空间内插变量的充分几何必要条件。在第二个方向上，他将使用插值的结果和方法来研究指数多项式，并获得Lojasiewicz型不等式，这与复谐分析中的一些重要猜想有关。在第三个方向上，他计划找到对整个全纯映射的零变体体积的估计，这与插值变体的几何方面密切相关。他还将研究运动目标的“精炼”奈万林纳第二基本定理，特别关注亚纯函数的唯一性问题和（偏）微分方程的亚纯解。在信号处理、图像压缩和其他应用中出现的卷积方程系统的许多重要问题，如找到所有分布解（或找出是否有分布解），都可以转化为具有生长条件的整个函数的插值问题。题目本身就是几个复杂变量中的主要问题之一。本文的研究目标是在几个复杂变量及其应用方面丰富和推进上述领域。