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 languageEnglish
Pages (from-to)85-96
Number of pages12
JournalMathematics of the USSR - Sbornik
Volume64
Issue number1
DOIs
StatePublished - 28 Feb 1989
Externally publishedYes

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