华东师范大学学报(自然科学版) ›› 2013, Vol. 2013 ›› Issue (1): 17-23.

• 应用数学与基础数学 • 上一篇    下一篇

极体的体积确定凸体

吴力荣   

  1. 浙江工业职业技术学院, 浙江~~绍兴 312000
  • 收稿日期:2012-03-01 修回日期:2012-06-01 出版日期:2013-01-25 发布日期:2013-01-18

Determination of a convex body by the volume of its polar bodies

WU Li-rong   

  1. Zhejiang Industry Polytechnic College, Shaoxing Zhejiang 312000, China
  • Received:2012-03-01 Revised:2012-06-01 Online:2013-01-25 Published:2013-01-18

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摘要： 利用球面调和函数和\,Hamburger\,矩方法, 证明了,
${\mathbb{R}}^{n}$\,中一个包含半径为\,$\delta$\,的球的原点对称凸体,
能被其在此球附近的所有点的极体的体积所唯一确定.

关键词: 凸体, 体积, 极体

Abstract: Using tools of spherical harmonics and Hamburger's moment,
we proved that an origin-symmetric convex body containing a sphere
of radius $\delta$ in its interior is determined in
${\mathbb{R}}^{n}$ by the volume of its polar bodies with respect to
all the points near the sphere.

Key words: convex body, volume, polar body

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