The Knaster problem and the geometry of high-dimensional cubes

被引：13
|
作者：
Kashin, BS
Szarek, SJ
机构：
[1] VA Steklov Math Inst, Moscow 117966, Russia
[2] Univ Paris 06, Equipe Anal Fonctionnelle, F-75252 Paris, France
[3] Case Western Reserve Univ, Dept Math, Cleveland, OH 44106 USA
来源：
COMPTES RENDUS MATHEMATIQUE | 2003年 / 336卷 / 11期
关键词：
D O I：
10.1016/S1631-073X(03)00226-7
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We study questions of the following type: Given positive semi-definite matrix G, does there exist a sequence of vectors in R-n whose Grammian equals to !; and which has some specified additional properties (typically related to the sup norm)? In particular, we show that the answer to the 1947 Knaster problem about real functions on spheres is negative for sufficiently large dimensions. (C) 2003 Academie des sciences. Published by Editions scientifiques et medicales Elsevier SAS. All rights reserved.
引用
收藏
页码：931 / 936
页数：6
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