Mathematical Sciences: Microlocal Approaches to Spectral Problems II

数学科学：谱问题的微局域方法 II

• 批准号: 9107600
• 负责人: Alejandro Uribe
• 金额: $ 2.72万
• 依托单位: Regents of the University of Michigan - Ann Arbor
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1991
• 资助国家: 美国
• 起止时间: 1991-09-15 至 1994-02-28
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9107600&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Microlocal; Approaches; Spectral

Professor Uribe will continue his research on problems in global analysis. In particular he will study the spectral asymptotics of elliptic operators and their relationships with symplectic geometry. One main problem is to relate the asymptotic properties of the Schrodinger operator to the classical mechanics of the system represented by the operator. A second problem is to develop the theory of the Fourier integral operator in the setting of quantized Kahler manifolds. The motivation for this research comes from mathematical physics and inverse spectral problems. Inverse spectral theory tries to understand an operator by studying how the operator separates input into discrete parts. The Schrodinger operator in particular plays a central role in the modeling of many physical systems and a better understanding of the spectral properties of this operator would have broad application.

乌里韦教授将继续他对全球分析中问题的研究。特别是，他将研究椭圆算子的谱渐近性及其与辛几何的关系。一个主要问题是将薛定谔算子的渐近性质与该算子所代表的系统的经典力学联系起来。第二个问题是发展量子化Kahler流形背景下的傅立叶积分算子理论。这项研究的动机来自数学物理和逆谱问题。逆谱理论试图通过研究运算符如何将输入分离为离散部分来理解运算符。特别是薛定谔算符在许多物理系统的建模中起着核心作用，更好地理解该算符的光谱性质将具有广泛的应用。