Geodesic
Separation by Convex Interpolation Families
Journal of convex analysis, Tome 20 (2013) no. 4, pp. 937-946

Voir la notice de l'article provenant de la source Heldermann Verlag

A set of continuous functions defined on an interval I is called an n-parameter Beckenbach family, if each n points of I × R (with pairwise distinct first coordinates) can be interpolated by a unique element of the set. The aim of the present note is to characterize such pairs of real valued functions that can be separated by a member of a given convex Beckenbach family of order n. The key idea of the proof is to identify the family with Rn via a suitable homeomorphism. Then, the classical Helly Theorem guarantees the existence of a proper separator.
Classification : 26A51, 39B62, 52A20
Mots-clés : Interpolation families, Haar and Chebyshev systems, Separation theorems, Helly's Theorem 
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     author = {M. Bessenyei and P. Szokol},
     title = {Separation by {Convex} {Interpolation} {Families}},
     journal = {Journal of convex analysis},
     pages = {937--946},
     publisher = {mathdoc},
     volume = {20},
     number = {4},
     year = {2013},
     url = {http://geodesic.mathdoc.fr/item/JCA_2013_20_4_JCA_2013_20_4_a2/}
}
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M. Bessenyei; P. Szokol. Separation by Convex Interpolation Families. Journal of convex analysis, Tome 20 (2013) no. 4, pp. 937-946. http://geodesic.mathdoc.fr/item/JCA_2013_20_4_JCA_2013_20_4_a2/