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: 0100486
• 负责人: B L
• 金额: --
• 依托单位: Florida International University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2001
• 资助国家: 美国
• 起止时间: 2001-07-01 至 2005-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0100486&HistoricalAwards=false
• 关键词: Entire; Meromorphic; Functions; Several; Complex

The proposed research is directed at topics in several complex variables onentire holomorphic maps, interpolation problems, and value distribution theory.The principle investigator proposes to continue his study on the well-knowntranscendental Bezout problem about the growth of the volume of entire analyticsets and find sharp estimates on the counting functions of zeros of entireholomorphic maps. He also proposes to study interpolation problems for weighted spaces of entire functions, one of fundamental and central problems in several complex variables. In particular, he wishes to characterize interpolatingvarieties geometrically, which is closely tied with his study on the Bezoutproblem. In the third direction, he would like to continue his research on valuedistribution theory with a special attention given to the refined Nevanlinnasecond fundamental theorem for slowly moving targets and its relations to otherproblems such as uniqueness problems of meromorphic functions and meromorphic solutions of partial differential equations.The above problems are important not just from the point of view of severalcomplex variables, but also from their relations and applications to othersubjects such as harmonic analysis, transcendental number theory, systems theory and engineering. For instance, many important problems like finding andrepresenting solutions to partial differential equations or systems ofconvolution equations arising in signal processing, image compression, materialstesting, etc. are equivalent to interpolation problems for entire functions inweighted spaces. The proposed research aims at developing and advancing boththeories and applications for the above areas in several complex variables.

本论文的主要研究方向是全纯映射上的多复变量问题、插值问题和值分布理论，主要研究方向是继续研究关于全解析集体积增长的超越Bezout问题，并找到全纯映射零点计数函数的精确估计。他还建议研究加权空间的整个功能，一个基本的和中心的问题，在几个复杂的变量。特别是，他希望刻画interpolatingvariants几何，这是密切联系在一起，他的研究Bezout问题。在第三个方向，他想继续他的研究价值分布理论，特别注意到细化的Nevanlinnasecond基本定理缓慢移动的目标和它的关系，以其他问题，如唯一性问题的亚纯函数和亚纯解偏微分方程。上述问题是重要的，不仅从角度来看，几个复杂的变量，也包括它们与调和分析、超越数论、系统论和工程等学科的关系和应用。例如，在信号处理、图像压缩、材料测试等领域中，许多重要的问题，如偏微分方程或卷积方程组的求解和表示，都等价于加权空间中整函数的插值问题。本研究旨在发展和推进多复变函数在上述领域的理论和应用。