Minimal affine boundaries of convex sets
type: Item
instance of: scholarly article
title: Minimal affine boundaries of convex sets
zbMATH Open document ID: 0662.46010
published in: Tokyo Journal of Mathematics
publication date: 1988-01-01T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 46A55
Mathematics Subject Classification ID: 46J20
Mathematics Subject Classification ID: 32A40
zbMATH DE Number: 4082257
zbMATH Keywords: affine functions
zbMATH Keywords: extreme sets
zbMATH Keywords: minimum principle
zbMATH Keywords: minimal affine n- boundary
zbMATH Keywords: compact convex sets
zbMATH Keywords: real locally convex linear space
zbMATH Keywords: function algebra boundaries
author: Thomas V. Tonev
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.3836/tjm/1270134272
OpenAlex ID: W2059227685
DOI: 10.3836/TJM/1270134272
description: scientific article; zbMATH DE number 4082257