Onextensions of the Gale-Berlekamp switching problem and constants ofl q —spaces期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

Onextensions of the Gale-Berlekamp switching problem and constants ofl q —spaces

Authors:	Y. Gordon H. S. Witsenhausen

Affiliation:	(1) Hebrew University of Jerusalem, Jerusalem;(2) Louisiana State University, Louisiana, USA;(3) Bell Telephone Laboratories, Inc., Murray Hill, N. J.

Abstract:	For positive integersn, m and realp≥1, let $B_p (n, m) = mathop {min }limits_{varepsilon i j = pm 1} mathop {max }limits_{theta _{ i} = pm 1} left( {sumlimits_{j = 1}^m {\| } sumlimits_{i = 1}^n {theta _i varepsilon _{ij} } \|^p } right)^{1/p}$ Upper and lower bounds for this quantity are derived, extending results of Brown and Spencer forB ₁(n,n), corresponding to the Gale-Berlekamp switching problem. For a Minkowski spaceM of dimensionm, define $delta (M) = mathop {min }limits_{\|\|x_i \|\| = 1} mathop {max }limits_{theta _i = pm 1} \|\|sumlimits_{i = 1}^m {theta _i x_i }$ a quantity investigated by Dvoretzky and Rogers.

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