Problems in Analysis Related to P.D.E., Geometry, and Several Complex Variables

与偏微分方程、几何和多个复变量相关的分析问题

• 批准号: 0245242
• 负责人: Charles Fefferman
• 金额: $ 66.2万
• 依托单位: Princeton University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2003
• 资助国家: 美国
• 起止时间: 2003-07-01 至 2007-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0245242&HistoricalAwards=false
• 关键词: Problems; Analysis; Related; P.D.E.; Geometry

Abstract DMS-0245242Charles Fefferman and Elias Stein Problems in analysis Among the problems that will be investigated are:(1) The domination of pseudo-differential operators.(2) Singular integrals which have that singularities on flag manifolds, and their application to several complex manifolds.(3) Classification of conformal manifolds analogous to Branson's Q curvature.(4) Estimates for oscillatory integrals and questions of stability.(5) Efficient hedging strategies in the presence of transaction costs. The methods of harmonic analysis and partial differential equations have important applications in many fields of science, for example physics, engineering, and finance; also in different parts of mathematics, for example geometry. The underlying reason is that partial differential equations express the laws which govern a wide variety of phenomena, while harmonic analysis is a central tool to understand the solutions of the equations.

摘要 DMS-0245242查尔斯·费曼和埃利亚斯·斯坦 分析中的问题在将要研究的问题中有：（1）伪微分算子的控制。(2)旗流形上具有奇异性的奇异积分及其在几种复流形上的应用。(3)类似于Branson Q曲率的共形流形的分类。(4)振荡积分的估计与稳定性问题。(5)存在交易成本时的有效套期保值策略。调和分析和偏微分方程的方法在许多科学领域都有重要的应用，例如物理学、工程学和金融学;也在数学的不同部分，例如几何学。 其根本原因是偏微分方程表达了支配各种现象的定律，而调和分析是理解方程解的核心工具。