Harmonic Analysis and Partial Differential Operators

谐波分析和偏微分算子

• 批准号: DP140100649
• 负责人: Prof Xuan Thinh Duong
• 金额: $ 25.54万
• 依托单位: Macquarie University
• 依托单位国家: 澳大利亚
• 项目类别: Discovery Projects
• 财政年份: 2014
• 资助国家: 澳大利亚
• 起止时间: 2014-01-01 至 2017-12-31
• 项目状态: 已结题
• 来源: https://dataportal.arc.gov.au/RGS/Web/Grants/DP140100649
• 关键词: Harmonic; Analysis; Partial; Differential; Operators

Harmonic Analysis has played an important role in the study of partial differential equations, operator theory, function spaces with wide applications. This project aims to study partial differential equations with non-smooth coefficients on domains with rough boundaries and on general metric spaces. The proposed problems are at the frontier of harmonic analysis and spectral analysis. Expected outcomes are solutions to a number of key long-standing open problems in harmonic analysis, new original ideas and new techniques with wide scopes of applications in mathematical research.

谐波分析在研究部分微分方程，运算符理论，功能空间的研究中发挥了重要作用。该项目旨在研究具有粗糙边界和一般度量空间的域上具有非平滑系数的部分微分方程。提出的问题位于谐波分析和光谱分析的前沿。预期的结果是谐波分析，新的原始思想和新技术的许多关键长期开放问题的解决方案，并具有广泛的数学研究应用程序。