Geodesic
Incoherent systems and coverings in finite dimensional Banach spaces
Sbornik. Mathematics, Tome 205 (2014) no. 5, pp. 703-721

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We discuss the construction of coverings of the unit ball of a finite dimensional Banach space. There is a well-known technique based on comparing volumes which gives upper and lower bounds on covering numbers. However, this technique does not provide a method for constructing good coverings. Here we study incoherent systems and apply them to construct good coverings. We use the following strategy. First, we build a good covering using balls with a radius close to one. Second, we iterate this construction to obtain a good covering for any radius. We shall concentrate mainly on the first step of this strategy. Bibliography: 14 titles.
Keywords: incoherent systems, covering of balls, Banach space, modulus of smoothness
Mots-clés : explicit constructions. 
@article{SM_2014_205_5_a5,
     author = {V. N. Temlyakov},
     title = {Incoherent systems and coverings in finite dimensional {Banach} spaces},
     journal = {Sbornik. Mathematics},
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     publisher = {mathdoc},
     volume = {205},
     number = {5},
     year = {2014},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2014_205_5_a5/}
}
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V. N. Temlyakov. Incoherent systems and coverings in finite dimensional Banach spaces. Sbornik. Mathematics, Tome 205 (2014) no. 5, pp. 703-721. http://geodesic.mathdoc.fr/item/SM_2014_205_5_a5/