Mathematical Sciences: Structure Theory of Infinite Dimensional Banach Spaces and a Gaussian Correlation Problem

研究者的建议包括两部分。第一部分讨论了无限维巴拿赫空间理论中的几个问题。近四年来，巴拿赫空间结构理论的发展带来了令人兴奋的结果和新的问题。本建议的第二部分处理高斯相关问题。一个植根于统计学的老问题是估计（可能相关的）高斯变量的多维置信区域。这个问题可以用更几何的语言来表述。也就是说，在n维空间中两个对称凸集的交集的高斯测度是否大于或等于它们的测度之积。该提案包括两个部分。第一部分介绍了作者在无限维巴拿赫空间理论方面的工作，这是近年来取得令人兴奋和惊人成果的领域。第二部分涉及一个起源于统计学的老问题。即从下面估计多维正态分布的置信区域。＊＊＊

9501243 Schlumprecht The investigator's proposal contains two parts. The first part discusses some problems in infinite dimensional Banach space theory.The developments in structure theory of Banach spaces over the last four years led to exciting results and new problems.The second part of this proposal treats a Gaussian correlation problem. An old question, rooted in statistics, is to estimate multidimensional confidence regions of (possibly dependent) Gaussian variables. This question can be formulated in a more geometrical language. Namely, whether or not the Gausssian measure of the intersection of two symmetric, convex sets in an n dimensional space is bigger than or equal to the product of their measures. The proposal has two parts. The first part presents a continuation of the proposers work in infinite dimensional Banach space theory, a field in which exciting and astonishing results were achieved in recent years. The second part deals with an old question originating in Statistics. Namely to estimate confidence regions for multidimensional normal distributions from below. ***