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Mat. Sb., 2014, Volume 205, Number 5, Pages 97–116 (Mi msb8242)  

This article is cited in 1 scientific paper (total in 1 paper)

Incoherent systems and coverings in finite dimensional Banach spaces

V. N. Temlyakovab

a Steklov Mathematical Institute of the Russian Academy of Sciences
b University of South Carolina

Abstract: 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, explicit constructions.

Funding Agency Grant Number
National Science Foundation DMS-1160841


DOI: https://doi.org/10.4213/sm8242

Full text: PDF file (541 kB)
References: PDF file   HTML file

English version:
Sbornik: Mathematics, 2014, 205:5, 703–721

Bibliographic databases:

Document Type: Article
UDC: 514.174.3+517.982.22
MSC: Primary 52C17; Secondary 05B40
Received: 23.04.2013 and 20.11.2013

Citation: V. N. Temlyakov, “Incoherent systems and coverings in finite dimensional Banach spaces”, Mat. Sb., 205:5 (2014), 97–116; Sb. Math., 205:5 (2014), 703–721

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. V. N. Temlyakov, “Dictionary descent in optimization”, Anal. Math., 42:1 (2016), 69–89  mathnet  crossref  mathscinet  zmath  isi  elib  scopus
  • Математический сборник Sbornik: Mathematics (from 1967)
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