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Sbornik: Mathematics, 2014, Volume 205, Issue 5, Pages 703–721
DOI: https://doi.org/10.1070/SM2014v205n05ABEH004395 (Mi sm8242) 		 
This article is cited in 2 scientific papers (total in 2 papers)

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
English version PDF (502 kB) Citations (2)
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DOI: https://doi.org/10.1070/SM2014v205n05ABEH004395
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
Received: 23.04.2013 and 20.11.2013
Russian version:
Matematicheskii Sbornik, 2014, Volume 205, Number 5, Pages 97–116
DOI: https://doi.org/10.4213/sm8242
Bibliographic databases:
Document Type: Article
UDC: 514.174.3+517.982.22
MSC: Primary 52C17; Secondary 05B40
Language: English
Original paper language: Russian
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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  • https://www.mathnet.ru/eng/sm/v205/i5/p97
    • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    Russian version PDF:163
    English version PDF:24
    References:68
    First page:36
     
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