Geodesic
On the Algebraic Properties of Convex Bodies and Some Applications
Journal of convex analysis, Tome 7 (2000) no. 1, pp. 129-166 Cet article a éte moissonné depuis la source Heldermann Verlag

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We extend the set of convex bodies up to differences (factorized pairs) of convex bodies; thereby (Minkowski) multiplication by real scalar is extended in a natural way. We show that differences of convex bodies form a special quasilinear space with group structure. The latter is abstractly studied by introducing analogues of linear combinations, dependence, basis, associated linear spaces etc. A theorem of H. Radström for embedding of convex bodies in a normed vector space is generalized. Support functions and their differences are discussed in relation to quasilinear spaces.
Classification : 52A01, 52A05, 06F20, 15A03, 65G10
Mots-clés : Differences of convex bodies, Minkowski operations, quasilinear spaces, differences of support functions 
@article{JCA_2000_7_1_JCA_2000_7_1_a6,
     author = {S. Markov},
     title = {On the {Algebraic} {Properties} of {Convex} {Bodies} and {Some} {Applications}},
     journal = {Journal of convex analysis},
     pages = {129--166},
     year = {2000},
     volume = {7},
     number = {1},
     url = {http://geodesic.mathdoc.fr/item/JCA_2000_7_1_JCA_2000_7_1_a6/}
}
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S. Markov. On the Algebraic Properties of Convex Bodies and Some Applications. Journal of convex analysis, Tome 7 (2000) no. 1, pp. 129-166. http://geodesic.mathdoc.fr/item/JCA_2000_7_1_JCA_2000_7_1_a6/