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.

摘要：PAN PAN的调查将集中在各种单数积分和振荡性积分运算符上，这些积分和振荡性积分算子在谐波分析和相关领域的许多问题中自然出现，包括复杂分析和偏微分方程的理论。随着对数学问题的大量问题的应用，这些积分因其重要性而获得了越来越多的认可。尽管该领域的研究是密集和富有成果的，但还有更多待理解。该项目将涵盖当前感兴趣的许多主题，完成后，该项目将大步向往这些操作员的全面理解以及数学分析中的相关问题。 所研究的对象构成了物理现象的数学建模的重要组成部分，例如热传导和波动运动。它们还出现在涉及电路和信号处理的工程问题中。因此，了解此类物体不仅具有理论价值观，而且还将在其他科学和工程领域提供指导。