Spectral Theory

西蒙教授将研究正交多项式谱理论中的各种问题。他打算研究与自相似测度（如康托测度）相关的多项式的零结构，从而将其与最近在动力系统和谐波分析方面的研究联系起来。他还打算超越实线和单位圆的经典光谱理论体系。这项研究利用了西蒙教授及其同事最近的进展，将其扩展到新的方向。正交多项式对科学和工程的广泛领域产生了影响，包括电气工程中的滤波器理论、统计学问题，以及最近的量子计算问题。西蒙教授所做的基础研究，在这些更实用的领域有长期的衍生成果。西蒙教授直接指导了三十多名研究生，并指导了大约三十多名博士后。他的论文和书籍具有相当大的影响力，在MathSciNet上被引用了8645次（大约在过去的十年里）。他是为数不多的被引用超过5000次的数学家之一。

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.