Minimal affine boundaries of convex sets
The paper introduces and studies the concept of the minimal affine n- boundary \(E_ n(M)\) of a compact convex sets M in a real locally convex linear space V. The set \(E_ 1(M)\) is the closed convex hull of the extreme points of M. The set \(E_ n(M)\) is the intersection of those closed subset E of M such that for every ``regular'' n-tuple \((f_ 1,...,f_ n)\) of continuous affine functions on M the Euclidean norm of \((f_ 1(x),...,f_ n(x))\) attains its infinimum on E. The author gives alternative descriptions of \(E_ n(M)\) and relates this concept to function algebra boundaries.
scientific article; zbMATH DE number 4082257