Mathematical Sciences: Operators on Spaces of Analytic Functions

数学科学：解析函数空间上的运算符

• 批准号: 9622914
• 负责人: William Ross
• 金额: $ 3万
• 依托单位: University of Richmond
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1996
• 资助国家: 美国
• 起止时间: 1996-07-15 至 1998-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9622914&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Operators; Spaces; Analytic

DMS-9622914 PI: William Ross University of Richmond The principal investigator will conduct research on operators on spaces of analytic functions. Such problems explore the relationship between functional analysis and complex function theory. The first part of the proposal examines the invariant subspaces of the "backward shift operator" on a general Hilbert space of analytic functions. In the second part of the proposal, the principal investigator plans to examine the Bergman space on a "crescent" domain and examine certain subspaces which are invariant under the linear transformation "multiplication by z". In the third part of the proposal, the principal investigator plans to look at the closure of the polynomials on the "standard crescent" (the region bounded by two internally tangent circles). As mentioned earlier, these types of problems combine two fields of mathematics, functional analysis and complex function theory. This link was first noticed by Arne Beurling in 1949 in his seminar paper on the shift operator. Further results on the shift were taken up by several Russians such as Korenblum, Nikolskii, Havin, Shirokov, and Shamoyan. In this proposal we examine these same problems but will pay closer attention to the geometry involved.

DMS-9622914 PI：威廉·罗斯·里士满大学主要研究人员将对分析功能空间的操作员进行研究。此类问题探讨了功能分析与复杂功能理论之间的关系。该提案的第一部分研究了分析功能的一般希尔伯特空间上“向后移动算子”的不变子空间。在提案的第二部分中，主要研究者计划检查“新月”域上的伯格曼空间，并检查某些在线性变换“乘以z”下不变的子空间。 在提案的第三部分中，首席研究员计划在“标准新月”（由两个内部切线圈界定的区域）上查看多项式的关闭。 如前所述，这些类型的问题结合了两个数学领域，功能分析和复杂功能理论。 Arne Beurling在1949年在他的有关Shift Operator的研讨会上首次注意到了这一链接。这次转变的进一步结果是由Korenblum，Nikolskii，Havin，Shirokov和Shamoyan等几个俄罗斯人取得的。 在此提案中，我们研究了这些相同的问题，但会密切关注所涉及的几何形状。