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Mathematics of the USSR-Sbornik, 1989, Volume 64, Issue 1, Pages 85–96
DOI: https://doi.org/10.1070/SM1989v064n01ABEH003295
(Mi sm1729)
 

This article is cited in 70 scientific papers (total in 70 papers)

Extremal properties of orthogonal parallelepipeds and their applications to the geometry of Banach spaces

E. D. Gluskin
References:
Abstract: It is proved that the distribution function for the maximum of the modulus of a set $n$ of jointly Gaussian random variables with given variance and zero mean is minimal if these variables are independent. For $n\leqslant N$ let
$$ \alpha_{N,n}=\sup_{x_1,\dots,x_N\in B_2^n}\inf_{z\in S^{n-1}}\sup_{1\leqslant j\leqslant N}|\langle x_j,z\rangle|. $$
As a corollary of the result mentioned, the precise orders of the constants $\alpha_{N,n}$ are computed $\alpha_{N,n}\asymp\min\{1,\sqrt{n^{-1}\log(1+N/n)}\}$, and various improvements of these inequalities are obtained. The estimates are used in particular to construct lacunary analogues of the Rudin–Shapiro trigonometric polynomials.
Bibliography: 23 titles.
Received: 30.04.1987
Russian version:
Matematicheskii Sbornik. Novaya Seriya, 1988, Volume 136(178), Number 1(5), Pages 85–96
Bibliographic databases:
Document Type: Article
UDC: 517.5
MSC: Primary 46B20, 51M25; Secondary 60G15
Language: English
Original paper language: Russian
Citation: E. D. Gluskin, “Extremal properties of orthogonal parallelepipeds and their applications to the geometry of Banach spaces”, Mat. Sb. (N.S.), 136(178):1(5) (1988), 85–96; Math. USSR-Sb., 64:1 (1989), 85–96
Citation in format AMSBIB
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\by E.~D.~Gluskin
\paper Extremal properties of orthogonal parallelepipeds and their applications to the geometry of Banach spaces
\jour Mat. Sb. (N.S.)
\yr 1988
\vol 136(178)
\issue 1(5)
\pages 85--96
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\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=945901}
\zmath{https://zbmath.org/?q=an:0668.52002|0648.52003}
\transl
\jour Math. USSR-Sb.
\yr 1989
\vol 64
\issue 1
\pages 85--96
\crossref{https://doi.org/10.1070/SM1989v064n01ABEH003295}
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\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-0002542941}
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  • https://doi.org/10.1070/SM1989v064n01ABEH003295
  • https://www.mathnet.ru/eng/sm/v178/i1/p85
  • This publication is cited in the following 70 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics
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    Abstract page:1303
    Russian version PDF:366
    English version PDF:42
    References:103
     
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