极体的体积确定凸体

利用球面调和函数和Hamburger矩方法,证明了,Rⁿ中一个包含半径为δ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.

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

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.