权益分类	功能权益	普通用户	{{item.name}}会员
{{category.name}}	{{benefitItem.name}}

Linear Analysis, Complex Analysis, and Number Theory

线性分析、复分析和数论

基本信息

批准号：
0070603
负责人：
Louis de Branges
金额：
$ 3.6万
依托单位：
Purdue Research Foundation
依托单位国家：
美国
项目类别：
Standard Grant
财政年份：
2000
资助国家：
美国
起止时间：
2000-06-15 至 2002-11-30
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=0070603&HistoricalAwards=false
关键词：
Linear Analysis Complex Number Theory

项目摘要

ABSTRACT:The principal research initiative results from a theory of Hilbert spaces of entire functions produced in the postdoctoral years 1957--1962 and from a related theory of Hilbert spaces of analytic functions then produced in joint work with James Rovnyak. A striking application was made in 1984 to a proof of the Bieberbach conjecture. Another research initiative results from a proof obtained in 1959 of the Stone--Weierstrass theorem. An application to the invariant subspace problem was made in 1991 by Victor Lomonosov. Existence theorems for invariant subspaces are currently pursued by methods of the Stone--Weierstrass theorem and of Hilbert--spaces of analytic functions.Hilbert spaces of entire functions are being applied to a proof of the Riemann hypothesis.The significance of the present work lies in its effective combination oftwo research concepts, a classical concept whose aim is to solve difficult problems, and a modern concept whose aim is to introduce innovativetechniques. The test of success is measured by the successful application ofnew methods to old problems. The Riemann hypothesis has been a consistent aim of the present work since the doctoral thesis. A successful conclusion ofthis longstanding project would be a major contribution to mathematics.

摘要：主要的研究活动的结果，从理论的希尔伯特空间的整个功能产生的博士后年1957年至1962年，并从一个相关的理论希尔伯特空间的解析函数，然后产生在联合工作与詹姆斯Rovnyak。一个引人注目的应用是在1984年证明了比伯巴赫猜想。另一项研究倡议的结果，证明在1959年获得的石头-维尔斯特拉斯定理。应用不变子空间问题是在1991年由维克托罗蒙诺索夫。不变子空间的存在性定理目前是用Stone-Weierstrass定理和Hilbert-解析函数空间的方法来研究的。整函数的Hilbert空间正被用来证明Riemann假设。本工作的意义在于它有效地结合了两个研究概念，一个是解决难题的经典概念，一个是解决问题的经典概念。and a modern现代concept概念whose其aim目的is to introduce介绍innovative革新techniques技术.对成功的检验是通过新方法成功地应用于老问题来衡量的。黎曼假设一直是一个一贯的目标，目前的工作，因为博士论文。这一长期项目的圆满结束将是对数学的重大贡献。