Please use this identifier to cite or link to this item: http://hdl.handle.net/10016/6443

 Google™ Scholar. Others By: Portilla, Ana - Quintana, Yamilet - Rodríguez, José M. - Tourís, Eva
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 Title: Weighted Weierstrass' theorem with first derivatives Author(s): Portilla, AnaQuintana, YamiletRodríguez, José M.Tourís, Eva Publisher: Elsevier Issued date: 15-Oct-2007 Citation: Journal of Mathematical Analysis and Applications, 2007, vol. 334, n. 2, p. 1167-1198 URI: http://hdl.handle.net/10016/6443 ISSN: 0022-247X DOI: 10.1016/j.jmaa.2006.12.066 Description: 32 pages, no figures.-- MSC2000 codes: 41A10, 46E35, 46G10.MR#: MR2338656 (2008g:41004)Zbl#: Zbl pre05173014 Abstract: We characterize the set of functions which can be approximated by continuous functions with the norm $\ \ {L infty(w)}$ for every weight w. This fact allows to determine the closure of the space of polynomials in $L infty(w)$ for every weight w with compact support. We characterize as well the set of functions which can be approximated by smooth functions with the norm$$\ \ {W 1,\infty}(w_0,w_1)}\coloneq \ \ {L infty(w_0)}+ \ '\ {L infty(w_1)},$$for a wide range of (even non-bounded) weights $w_0,w_1$. We allow a great deal of independence among the weights. Sponsor: Research by first (A.P.), third (J.M.R.) and fourth (E.T.) autors was partially supported by three grants from MEC (MTM 2006-11976, MTM 2006-13000-C03-02, MTM 2006-26627-E), Spain. Review: PeerReviewed Publisher version: http://dx.doi.org/10.1016/j.jmaa.2006.12.066 Keywords: Weierstrass' theoremWeightSobolev spacesWeighted Sobolev spaces Rights: © Elsevier Appears in Collections: DM - GAMA - Artículos de Revistas