Mathematical Sciences: Research Group in Banach Spaces and Related Areas

数学科学：巴纳赫空间及相关领域研究小组

• 批准号: 9306868
• 负责人: Nigel Kalton
• 金额: $ 3万
• 依托单位: University of Missouri-Columbia
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1993
• 资助国家: 美国
• 起止时间: 1993-07-01 至 1995-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9306868&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Research; Group; Banach

The purpose of this award is to support a conference at the University of Missouri on the interaction of Functional Analysis, Harmonic Analysis, and Probability Theory. Proceedings of the conference will be published. The core topic of the conference is Banach space theory, which is that part of mathematics that attempts to generalize to infinitely many dimensions the structure of 3-dimensional Euclidean (i.e.ordinary) space. The axioms for the distance function in a Banach space are more relaxed than those for Euclidean distance (For example, the "parallelogram law" is not required to hold.), and as a result, the "geometry" of a Banach space can be quite exotic. Much of the research in this area concerns studying the structure theory of Banach spaces.

这一奖项的目的是支持在密苏里大学举行的关于泛函分析、调和分析和概率理论相互作用的会议。会议纪要将予以公布。会议的核心话题是Banach空间理论，它是试图将三维欧几里得(即普通)空间的结构推广到无限多维的数学部分。Banach空间中距离函数的公理比欧几里德距离的公理要宽松得多(例如，不需要遵守“平行四边形定律”)，因此，Banach空间的“几何”可能是相当奇异的。这方面的许多研究都涉及到对Banach空间的结构理论的研究。