Banach Spaces and their Applications

Banach 空间及其应用

• 批准号: 0244515
• 负责人: Nigel Kalton
• 金额: $ 28.52万
• 依托单位: University of Missouri-Columbia
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2003
• 资助国家: 美国
• 起止时间: 2003-05-01 至 2007-04-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0244515&HistoricalAwards=false
• 关键词: Banach; Spaces; their; Applications

AbstractKaltonIn this proposal, the aim is to study a number of problemsrelated to Banach space theory and its applications. Partof the project deals with the theory of extensions of oneBanach space by another. For example it is planned to studythe problem of classifying those Banach spaces such thatevery minimal extension is trivial. This problem can bereformulated as a problem in approximation theory. It isalso planned to study applications to problems in thenonlinear theory of Banach spaces, related to problems ofexistence of uniform homeomorphisms between two Banachspaces or between their unit balls. In a somewhat differentdirection the proposer plans to continue his ongoingresearch on Rademacher-bounded families of operators withapplications to sectorial operators and semigroups.The theory of extensions can be considered in the followingterms. Suppose we are given a centrally symmetric solid inthree or more dimensions and we are allowed only to computeits cross-section by a slice in some directions and theshadow cast by the body in the perpendicular directions.This gives us some information about the solid, but does notpermit complete reconstruction. The idea of studyingextensions is to obtain more complete information about thebody under certain additional conditions. Many questions ofimportance in mathematical analysis and applications,although not formally expressed in this way, can bevisualized in terms of extensions. Sectorial operators areof importance in the basic theory of partial differentialequations of evolution type; such equations are veryimportant in physical applications. Typically a sectorialoperator is a differential operator acting on some suitablespace of functions. By understanding the properties ofsectorial operators and the semigroups they generate onegains a better understanding of the behavior of solutions ofcertain partial differential equations.

AbstractKaltonin这个建议是研究与Banach空间理论及其应用有关的许多问题。 该项目的一部分涉及另一个项目的扩展理论。 例如，计划研究对那些Banach空间进行分类的问题，例如最小的扩展是微不足道的。 在近似理论中，这个问题可能会被视为问题。 ISALSO计划研究对Banach空间的偶像理论中的问题的应用，这与两个Banachspaces之间或其单位球之间的同态同态的问题有关。 在有些不同的方向上，提议者计划继续他对由拉德马赫的运营商的家庭进行进行的研究，并对部门运营商和半群进行了应用。扩展理论可以在以下内容中考虑。 假设我们给出了三个或更多尺寸的中央对称的固体，并且只允许我们通过某些方向上的切片和垂直方向上施放的theShadow进行横截面。这提供了有关固体的一些信息，但是notpermit完整的完整惯例。 研究延迟的想法是在某些其他条件下获得有关该体育的更多完整信息。 数学分析和应用中的许多问题虽然不是以这种方式正式表达的，但可以从扩展方面进行审理。 部门运营商在进化类型的部分差异化基本理论中至关重要； 这种方程在物理应用中非常重要。 通常，部门操作器是作用于某些适用功能的差异操作员。 通过了解部门操作员的属性和半群，它们可以更好地理解解决方案的解决方案的行为。