Mathematical Sciences: Analysis on Spaces of Analytic Functions

数学科学：解析函数空间的分析

• 批准号: 8800823
• 负责人: Sheldon Axler
• 金额: $ 16.02万
• 依托单位: Michigan State University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1988
• 资助国家: 美国
• 起止时间: 1988-07-01 至 1991-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8800823&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Analysis; Spaces; Analytic

The theory of analytic functions of a complex variable (those that are expandable in power series, so roughly speaking the limits of complex polynomials) has enriched all of mathematics for over a century. Such functions enjoy many remarkable properties, for instance that their values at points inside a closed curve are determined completely by their values on the curve. It happens that such functions readily aggregate themselves into Hilbert spaces, and the theory of operators on Hilbert space gains extra vividness when specialized to these spaces of analytic functions. The investigators will study specific classes of operators on the Hardy, Bergman, and Dirichlet function spaces, as well as algebras of bounded analytic functions on the unit disc.

复变解析函数论 （那些在幂级数中可扩展的，所以粗略地说， 复杂多项式的极限）丰富了所有 数学研究了世纪。这些功能享受许多 显着的性质，例如，它们的值在点 在封闭曲线内，完全由它们的值决定 在曲线上。 碰巧的是，这些功能很容易聚集 希尔伯特空间，以及算子理论， 希尔伯特空间获得额外的生动时，专门为这些 解析函数空间 调查人员将研究 特定类别的运营商的哈代，伯格曼，和 Dirichlet函数空间，以及有界代数 单位圆盘上的解析函数。