|
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
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
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
Linking options:
https://www.mathnet.ru/eng/sm1729https://doi.org/10.1070/SM1989v064n01ABEH003295 https://www.mathnet.ru/eng/sm/v178/i1/p85
|
Statistics & downloads: |
Abstract page: | 1303 | Russian version PDF: | 365 | English version PDF: | 42 | References: | 103 |
|