Complex Interpolation and Complex Convexity

复数插值和复凸性

• 批准号: 8901861
• 负责人: Zbigniew Slodkowski
• 金额: $ 4.09万
• 依托单位: University of Illinois at Chicago
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1989
• 资助国家: 美国
• 起止时间: 1989-07-01 至 1992-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8901861&HistoricalAwards=false
• 关键词: Complex; Interpolation; Convexity

The notion of interpolation indicated by the title of Professor Slodkowski's mathematical research project may be explained as follows. Mathematical objects of many sorts frequently come not singly but in whole families, individual members of which are located by specifying the value of a parameter. (For instance, a famous family of Banach spaces is indexed by the set of real numbers greater than or equal to one, with plus infinity thrown in for completeness.) The general problem of interpolation is: given members of the family located by extreme values of the parameter, fill in all the rest in some natural, optimal way. The particular interpolation problems addressed by this project have fundamental implications for mathematical analysis. More specifically, these problems have to do with multivariable complex interpolation theory and some related aspects of complex convexity. They are divided into three broad categories. The problems in the first group deal with the interpolation of infinite-dimensional spaces, regularity questions, and interpolation of convex and polynomially convex sets. The second category of problems concerns polynomially convex hulls. The third has to do with multifunctions that satisfy analogues of the function-theoretic properties of analyticity and harmonicity.

的标题所表明的插值的概念 斯洛德科夫斯基教授的数学研究项目可能是 如下所述。各种各样的数学对象 经常不是单独出现，而是在整个家庭，个人 其成员通过指定 参数. (For例如，一个著名的Banach空间族是 由大于或等于一的一组真实的数字索引， （加上无穷大以求完整）。总 插值问题是：给定家庭成员位于 通过参数的极值，将所有其余部分填充到一些 自然，最佳的方式。特殊插值问题 该项目所解决的问题对以下方面具有根本性的影响： 数学分析 更具体地说，这些问题与 多变量复插值理论及相关 复杂凸性的方面。它们分为三大类 类别第一组中的问题涉及 无限维空间的插值，正则性 问题，以及凸和多项式凸的插值 集.第二类问题涉及多项式 凸壳第三个与多功能有关， 满足的函数理论性质的类似物 解析性和调和性。