On the local equatorial characterization of zonoids and intersection bodies

被引：9
|
作者：
Nazarov, Fedor [2 ]
Ryabogin, Dmitry [1 ]
Zvavitch, Artem [1 ]
机构：
[1] Kent State Univ, Dept Math, Kent, OH 44242 USA
[2] Michigan State Univ, Dept Math, E Lansing, MI 48824 USA
来源：
ADVANCES IN MATHEMATICS | 2008年 / 217卷 / 03期
基金：
美国国家科学基金会;
关键词：
convex bodies; Radon transform; cosine transform; Fourier transform;
D O I：
10.1016/j.aim.2007.08.013
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper we show that there is no local equatorial characterization of zonoids in odd dimensions. This gives a negative answer to the conjecture posed by W. Weil in 1977 and shows that the local equatorial characterization of zonoids may be given only in even dimensions. In addition we prove a similar result for intersection bodies and show that there is no local characterization of these bodies. Published by Elsevier Inc.
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页码：1368 / 1380
页数：13
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