论文标题
派的特征
A characterisation of zonoids
论文作者
论文摘要
让$ k $为$ r^n $的某个标准的单位球。对于任意方向的$ u \ in r^n $，有一个关联的单位球$ k_u $，它在旋转方面是旋转不变的，将$ u $固定为固定，称为$ u $ -spin $ k_u $。事实证明，$ k $是当且仅当它的所有旋转都是Zonoid时。
Let $K$ be a unit ball of some norm in $R^n$. For an arbitrary direction $u\in R^n$, there is associated a unit-ball $K_u$, which is rotationally invariant with respect to rotations keeping $u$ fixed, called the $u$-spin of $K_u$. It is proved that $K$ is a zonoid if and only if all of its spins are zonoids.
