dc.contributor |
Centre de Recerca Matemàtica |
dc.contributor.author |
Bondarenko, Andriy |
dc.contributor.author |
Prymak, A |
dc.contributor.author |
Radchenko, Danylo |
dc.date.accessioned |
2013-01-22T11:14:04Z |
dc.date.available |
2013-01-22T11:14:04Z |
dc.date.created |
2012-12-01 |
dc.date.issued |
2012-12-01 |
dc.identifier.uri |
http://hdl.handle.net/2072/205485 |
dc.format.extent |
12 p. |
dc.language.iso |
eng |
dc.publisher |
Centre de Recerca Matemàtica |
dc.relation.ispartofseries |
Prepublicacions del Centre de Recerca Matemàtica;1127 |
dc.rights |
info:eu-repo/semantics/openAccess |
dc.rights |
L'accés als continguts d'aquest document queda condicionat a l'acceptació de les condicions d'ús establertes per la següent llicència Creative Commons: http://creativecommons.org/licenses/by-nc-nd/3.0/es/ |
dc.source |
RECERCAT (Dipòsit de la Recerca de Catalunya) |
dc.subject.other |
Probabilitats |
dc.subject.other |
Grafs, Teoria dels |
dc.subject.other |
Conjunt, Funcions de |
dc.title |
On concentrators and related approximation constants |
dc.type |
info:eu-repo/semantics/preprint |
dc.subject.udc |
517 - Anàlisi |
dc.embargo.terms |
cap |
dc.description.abstract |
Pippenger [Pi77] 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 [KaRo83] 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 &b&R&/b&&sup&d&/sup& by linear functions, and
improve the estimate of this Whitney constant from 802 (proved by
Brudnyi and Kalton in [BrKa00] to 73. |