Mathematical Sciences: Analytic Function Spaces

数学科学：解析函数空间

• 批准号: 9401234
• 负责人: Liming Yang
• 金额: $ 3.5万
• 依托单位: Washington University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1994
• 资助国家: 美国
• 起止时间: 1994-07-01 至 1997-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9401234&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Analytic; Function; Spaces

9401234 Yang This award supports mathematical research investigating spaces of analytic functions and the operator obtained through multiplication by the identity function. The goals are to study the existence of nontangential limits for each function in the closure of the analytic polynomials in some power norm relativeto a measure and the properties of the shift operator on these spaces. In addition work will be done investigating the structure of invariant subspaces and self-duality. Further work focuses on the set of bounded point evaluations for the closure of rational functions with poles off a given compact set, approximation problems for "near" analytic function spaces and the spectral properties of the shift acting on the closure of theideal generated by the conjugate of the identity. The study of function spaces obtained as the closure of aclass of polynomials has a long history going back before Mergalyan. Its value derives from a combination of approximation results stated in more or less geometric terms. The domain of these investigations is confined to the use of analytic functions, requiring considerable expertise in the field of classical function theory and the modern field of Banach spaces. ***

9401234 Yang 该奖项支持研究解析函数空间以及通过乘以恒等函数获得的算子的数学研究。 目标是研究相对于度量的某些幂范数中解析多项式的闭包中每个函数的非切向极限的存在性以及这些空间上移位算子的属性。 此外，还将研究不变子空间和自对偶性的结构。 进一步的工作集中于极点偏离给定紧集的有理函数闭包的有界点评估集、“近”解析函数空间的逼近问题以及作用于恒等共轭生成的理想闭包的位移的谱特性。 对作为一类多项式的闭包而获得的函数空间的研究有着悠久的历史，可以追溯到 Mergalyan 之前。 它的值源自以或多或少的几何术语表述的近似结果的组合。 这些研究的领域仅限于解析函数的使用，需要经典函数理论领域和现代巴纳赫空间领域的大量专业知识。 ***