Spectral Theory

谱理论

• 批准号: 0968856
• 负责人: Barry Simon
• 金额: $ 34.5万
• 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: 2010
• 资助国家: 美国
• 起止时间: 2010-07-01 至 2014-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0968856&HistoricalAwards=false
• 关键词: Spectral; Theory

Professor Simon will study various problems in the spectral theory of orthogonal polynomials. He intends to study the zero structure of the polynomials associated to self-similar measures like the Cantor measure, thereby linking to recent research in dynamical systems and harmonic analysis. He also intends to look beyond the classical spectral theory regimes of the real line and unit circle. This research piggybacks on recent progress by Professor Simon and coworkers, extending it in new directions.Orthogonal polynomials have impacts on a wide swath of science and engineering, including filter theory in electrical engineering, problems in statistics, and recently, problems in quantum computing. The kinds of basic research that Professor Simon does, has long term spinoff in these more applied areas. Professor Simon has directly supervised over thirty graduate students and mentored about that number of postdocs. His papers and books have had considerable impact, as seen by the 8,645 citations in MathSciNet (over roughly the past ten years). He is one of a handful of mathematicians with over 5,000 citations.

西蒙教授将研究正交多项式光谱理论中的各种问题。 他打算研究与自相似措施（如Cantor Measure）相关的多项式的零结构，从而与动态系统和谐波分析的最新研究联系起来。 他还打算超越真实线和单元圈的经典光谱理论制度。 这项研究对西蒙教授和同事的最新进展进行了研究，将其扩展到新的方向上。正交多项式对广泛的科学和工程有影响，包括电气工程中的滤波器理论，统计问题以及最近的量子计算问题。 西蒙教授所做的基础研究类型在这些更应用的领域中具有长期的衍生作用。 西蒙教授直接监督了30名研究生，并向博士后数量进行了指导。 正如MathScinet中的8,645篇引文所示（大约十年来）所见，他的论文和书籍产生了很大的影响。 他是少数数学家中有5,000多名引用的人之一。