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Mat. Sb. (N.S.), 1988, Volume 136(178), Number 1(5), Pages 85–96 (Mi msb1729)  

This article is cited in 26 scientific papers (total in 26 papers)

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

E. D. Gluskin


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
$$ \alpha_{N,n}=\sup_{x_1,…,x_N\in B_2^n}\inf_{z\in S^{n-1}}\sup_{1\leqslant j\leqslant N}|\langle x_j,z\rangle|. $$
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.

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English version:
Mathematics of the USSR-Sbornik, 1989, 64:1, 85–96

Bibliographic databases:

Document Type: Article
UDC: 517.5
MSC: Primary 46B20, 51M25; Secondary 60G15
Received: 30.04.1987

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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\yr 1989
\vol 64
\issue 1
\pages 85--96
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  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
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