论文信息 - EXTREMAL PROPERTIES OF ORTHOGONAL PARALLELEPIPEDS AND THEIR APPLICATIONS TO THE GEOMETRY OF BANACH SPACES

EXTREMAL PROPERTIES OF ORTHOGONAL PARALLELEPIPEDS AND THEIR APPLICATIONS TO THE GEOMETRY OF BANACH SPACES

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.Bibliography: 24 titles.

E. Gluskin

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