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New Combinations of Convex Sets (1999)

McMullen, Peter

Springer

Geometriae dedicata 78 (1999), S. 1-19

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ISSN: 1572-9168

Keywords: convex set ; fibre combination ; polarity ; convex function ; convolution.

Source: Springer Online Journal Archives 1860-2000

Topics: Mathematics

Notes: 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 of Medium: Electronic Resource

URL: http://dx.doi.org/10.1023/A:1005019802841

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