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

小行星9501243 调查员的建议包括两个部分。第一部分 讨论了无穷维Banach空间中的若干问题 Banach空间结构理论的发展 在过去的四年里，取得了令人兴奋的成果， 问题。本建议的第二部分处理高斯相关性 问题.一个植根于统计学的老问题是估计 多维置信域（可能相关） 高斯变量 这个问题可以用更几何的语言来表述。也就是说，无论两个对称的， n维空间中的凸集 大于或等于其测度的乘积。 该提案有两个部分。第一部分介绍了一个 在无限维空间中的工作的延续 Banach空间理论，一个令人兴奋的领域， 近年来取得了惊人的成绩。的 第二部分涉及一个起源于统计学的老问题。 即估计多维正态分布的置信域 从下面分配。 ***

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. ***