On Concentrators and Related Approximation Constants

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Date
2013-06-10MFO Scientific Program
OWLF 2013Series
Oberwolfach Preprints;2013,14Author
Bondarenko, A. V.
Prymak, A.
Radchenko, D.
Metadata
Show full item recordOWP-2013-14
Abstract
Pippenger ([Pip77]) 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 [KR83]) 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 Rd by linear functions, and improve the estimate of this Whitney constant from 802 (proved by Brudnyi and Kalton in [BK00]) to 73.