Mathematical Sciences: Determinants and Other Spectral Invariants for Elliptic and Toeplitz Operators on Manifolds

数学科学：流形上椭圆和托普利茨算子的行列式和其他谱不变量

• 批准号: 9506057
• 负责人: Kate Okikiolu
• 金额: $ 7.5万
• 依托单位: Princeton University
• 依托单位国家: 美国
• 项目类别: Standard 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=9506057&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Determinants; Other; Spectral

PI: Okikiolu DMS-9506057 Okikiolu will investigate the connection between zeta-regularized determinants of certain elliptic operators on a manifold with boundary and certain Toeplitz determinants on the boundary. She has proved a Campbell-Hausdorff formula for elliptic operators and a related trace formula, and developed new methods for symbolic computation. She will now extend these results to manifolds with boundary. Okikiolu also has proved an analogue of the strong Szego limit theorem for spheres of dimension two and three, and will further generalize this result. Partial differential equations form a basis for mathematical modeling of the physical world. The role of mathematical analysis is not so much to create the equations as it is to provide qualitative and quantitative information about the solutions. This may include answers to questions about uniqueness, smoothness and growth. In addition, analysis often develops methods for approximation of solutions and estimates on the accuracy of these approximations.

PI：Okikiolu DMS-9506057 Okikiolu将调查zeta正则化的决定因素的某些椭圆算子的流形上的边界和某些Toeplitz决定因素的边界。 她证明了椭圆算子的坎贝尔-豪斯多夫公式和相关的迹公式，并开发了符号计算的新方法。 她现在将这些结果扩展到流形的边界。 Okikiolu还证明了类似的强Szego极限定理领域的二维和三维，并将进一步推广这一结果。 偏微分方程是物理世界数学建模的基础。 数学分析的作用与其说是建立方程，不如说是提供关于解的定性和定量信息。 这可能包括关于独特性，平滑性和增长的问题的答案。 此外，分析经常发展出解的近似方法和对这些近似的准确性的估计。