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New combinations of convex sets

McMullen, P; (1999) New combinations of convex sets. GEOMETRIAE DEDICATA , 78 (1) 1 - 19.

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Abstract

The family of convex sets in a (finite dimensional) real vector space admits several unary and binary operations - dilatation, intersection, convex hull, vector sum - which preserve convexity. These generalize to convex functions, where there are in fact further operations of this kind. Some of the latter may be regarded as combinations of two such operations, acting on complementary subspaces. In this paper, a general theory of such mixed operations is introduced, and some of its consequences developed.

Type:Article
Title:New combinations of convex sets
Keywords:convex set, fibre combination, polarity, convex function, convolution, BODIES
UCL classification:UCL > School of BEAMS > Faculty of Maths and Physical Sciences > Mathematics

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