Mathematical Sciences: Oscillatory Integrals, Singular Integrals, and Their Applications

数学科学：振荡积分、奇异积分及其应用

• 批准号: 9622979
• 负责人: Yibiao Pan
• 金额: $ 6.9万
• 依托单位: University of Pittsburgh
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1996
• 资助国家: 美国
• 起止时间: 1996-08-15 至 2000-01-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9622979&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Oscillatory; Integrals; Singular

Abstract: Pan Pan's investigation will be focused on various singular integral and oscillatory integral operators which arise naturally in many problems in harmonic analysis and related fields including complex analysis and the theory of partial differential equations. With applications to a large number of problems in mathematics, these integrals have received an increasing amount of recognition for their importance. While research in this area has been intensive and fruitful, much more remains to be understood. This project will cover many topics of current interest, which when finished will make a big stride toward the full understanding of these operators and related problems in mathematical analysis. The objects under investigation form an important part of the mathematical modeling of physical phenomena such as heat conducting and wave motion. They also appear in engineering problems involving electric circuits and signal processing. Thus, gaining understanding of such objects will not only have theoretical values but also provide guidance in other areas of science and engineering.

文摘：潘攀的研究将集中在各种奇异积分和振荡积分算子上，这些算子自然地出现在调和分析及其相关领域的许多问题中，包括复分析和偏微分方程组理论。随着数学中大量问题的应用，这些积分的重要性得到了越来越多的认可。虽然在这一领域的研究是密集和富有成果的，但仍有更多的事情有待了解。这个项目将涵盖许多当前感兴趣的主题，完成后将朝着充分理解这些运算符和数学分析中的相关问题迈出一大步。研究对象构成了热传导和波动等物理现象的数学模型的重要组成部分。它们也出现在涉及电路和信号处理的工程问题中。因此，对这类物体的理解不仅具有理论价值，还将在科学和工程的其他领域提供指导。