On concentrators and related approximation constants

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:402

Article

Bondarenko, A. V.^1,2  Prymak, A.³  Radchenko, D.^2,4 

[1] Ctr Recerca Matemat, Barcelona 08193, Spain

[2] Natl Taras Shevchenko Univ, Dept Math Anal, UA-01033 Kiev, Ukraine

[3] Univ Manitoba, Dept Math, Winnipeg, MB R3T 2N2, Canada

[4] Max Planck Inst Math, D-53111 Bonn, Germany

关键词: Probabilistic method;    Concentrator graphs;    Additive set functions;    Whitney constant;   

DOI  :  10.1016/j.jmaa.2013.01.019

来源: Elsevier

【 摘 要 】

Pippenger (1977) [3] showed the existence of (6m, 4m, 3m, 6)-concentrator for each positive integer m using a probabilistic method. We generalize his approach and prove existence of (6m, 4m, 3m, 5.05)-concentrator (which is no longer regular, but has fewer edges). We apply this result to improve the constant of approximation of almost additive set functions by additive set functions from 44.5 (established by Kalton and Roberts in (1983) [2]) to 39. We show a more direct connection of the latter problem to the Whitney type estimate for approximation of continuous functions on a cube in R-d by linear functions and improve the estimate of this Whitney constant from 802 (proved by Brudnyi and Kalton in (2000) [1]) to 73. (C) 2013 Elsevier Inc. All rights reserved.

【 授权许可】

Free