Spectral Theory

谱理论

• 批准号: 0652919
• 负责人: Barry Simon
• 金额: $ 20.4万
• 依托单位: California Institute of Technology
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2007
• 资助国家: 美国
• 起止时间: 2007-07-01 至 2010-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0652919&HistoricalAwards=false
• 关键词: Spectral; Theory

Professor Simon will continue his research into spectral theory, especially the spectral theory of orthogonal polynomials. This project will focus on the theory where the spectrum has a finite number of gaps. It will also study perturbations of periodic Schrodinger operators, a model of impurities in solids.Spectral theory concerns the relation of mathematical models to their "spectral characteristics" and includes such areas as computer tomography, sonar analysis, and scattering of subatomic particles. Orthogonal polynomials are the simplest paradigm; they are especially useful because the inverse problem--often difficult to even show has solutions--is so explicit. In addition, orthogonal polynomials on the unit circle (on which Professor Simon has written a book) are a central tool in electronic circuit filter design.

西蒙教授将继续研究光谱理论，尤其是正交多项式的光谱理论。该项目将集中于频谱具有有限差距的理论。 它还将研究定期施罗宾格运营商的扰动，这是一种固体中的杂质模型。谱理论涉及数学模型与其“光谱特征”的关系，并包括计算机断层扫描，声纳分析和亚原子颗粒的散射等领域。正交多项式是最简单的范式；它们特别有用，因为逆问题（通常很难显示的解决方案）是如此明确。 此外，单位圆圈上的正交多项式（西蒙教授写了一本书）是电子电路滤波器设计的中心工具。