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

E. D. Gluskin

doi:10.1070/SM1989v064n01ABEH003295

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

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Abstract

It is proved that the distribution function for the maximum of the modulus of a set of jointly Gaussian random variables with given variance and zero mean is minimal if these variables are independent. For let As a corollary of the result mentioned, the precise orders of the constants are computed, and various improvements of these inequalities are obtained. The estimates are used in particular to construct lacunary analogues of the Rudin-Shapiro trigonometric polynomials.

Original language	English
Pages (from-to)	85-96
Number of pages	12
Journal	Mathematics of the USSR - Sbornik
Volume	64
Issue number	1
DOIs	https://doi.org/10.1070/SM1989v064n01ABEH003295
State	Published - 28 Feb 1989
Externally published	Yes

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abstract = "It is proved that the distribution function for the maximum of the modulus of a set of jointly Gaussian random variables with given variance and zero mean is minimal if these variables are independent. For let As a corollary of the result mentioned, the precise orders of the constants are computed, and various improvements of these inequalities are obtained. The estimates are used in particular to construct lacunary analogues of the Rudin-Shapiro trigonometric polynomials.",

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

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