极体算子与M-加算子的极表示

Extremal representations of polar set and M-addition

研究了极体算子和M-加算子的极表示.对于R^n中的紧凸集K,证明了K^o=(ext K)^o.证明了当K,L为R^n中包含原点的凸体,M为R^2中第一象限中的凸体时,有K和L的M-加等于K和L的(bd M)-加.通过举出反例,说明当M不在第一象限或者K,L不包括原点时,二者不一定相等.

The extremal representations of the polar set and M-addition are studied.If K is a compact and convex subset of R^n,then we have K^o=(ext K)^o.It is proved that M-sum of K and L is equal to the(bd M)-sum,if K and L are convex bodies containing the origin and M is a convex body in the first quadrant of R^2.Moreover,by the counterexamples given in section 3,all these conditions cannot be removed.