Mathematical Sciences: Oscillatory and Singular Integrals in Analysis, Geometry, and Physics

数学科学：分析、几何和物理中的振荡积分和奇异积分

• 批准号: 9505399
• 负责人: Duong Phong
• 金额: $ 17.7万
• 依托单位: Columbia University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1995
• 资助国家: 美国
• 起止时间: 1995-07-01 至 1998-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9505399&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Oscillatory; Singular; Integrals

Phong DMS-9505399 Phong will investigate core problems on oscillatory and singular integrals, Radon transforms, Green's functions, and analyticity of generalized functions. He will study coalescent versuq uniform estimates for oscillatory integrals, the singular integral equations for large N field theories, and the problem of analytic continuation for divergent integrals on the moduli space of Riemann surfaces. He will also investigate potential connections with the cut-off phenomenon in probability theory, molecular collisions in chemistry, string theory, and two-dimensional models of quark confinement. The mathematics underlying this research is harmonic analysis, which has as its origins the attempt to approximate an arbitrary function by a linear combination of very regular, much in the way that a sound wave is approximated by a sum of its pure tones.

Phong DMS-9505399 Phong 将研究振荡积分和奇异积分、Radon 变换、格林函数以及广义函数的解析性等核心问题。 他将研究振荡积分的合并与均匀估计、大 N 场论的奇异积分方程，以及黎曼曲面模空间上发散积分的解析延拓问题。 他还将研究与概率论中的截止现象、化学中的分子碰撞、弦理论和夸克禁闭的二维模型的潜在联系。 这项研究的数学基础是谐波分析，它的起源是试图通过非常规则的线性组合来近似任意函数，就像声波通过其纯音的总和来近似一样。