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：William Ross里士满大学 首席研究员将对运营商进行研究 解析函数的空间。这些问题探讨了 泛函分析与复变函数理论的关系提案的第一部分考察了不变量 子空间的“向后移动算子”的一般希尔伯特空间的解析函数。在提案的第二部分，主要研究者计划研究“新月”域上的伯格曼空间，并研究在线性变换“乘以z”下不变的某些子空间。 在提案的第三部分，首席研究员 计划看看多项式的封闭性， “标准新月”（内部由两个 切圆）。 如前所述，这些类型的问题结合了联合收割机和 数学、泛函分析和复变函数领域 理论这种联系是阿恩·伯林在1949年首先注意到的 在他关于移位运算符的研讨会论文中。有关的进一步结果 几个俄罗斯人， Nikolskii，Havin，Shirokov，and Shamoyan. 在这个建议中，我们将研究这些相同的问题，但将更密切地注意所涉及的几何形状。