Please use this identifier to cite or link to this item: http://hdl.handle.net/10016/6483

 Google™ Scholar. Others By: Rodríguez, José M. - Romera, Elena - Pestana, Domingo - Álvarez, Venancio
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 Title: Generalized weighted Sobolev spaces and applications to Sobolev orthogonal polynomials, II Author(s): Rodríguez, José M.Romera, ElenaPestana, DomingoÁlvarez, Venancio Publisher: Springer Issued date: Jun-2002 Citation: Approximation Theory and its Applications, 2002, vol. 18, n. 2, p. 1-32 URI: http://hdl.handle.net/10016/6483 ISSN: 1000-9221 (Print)1573-8175 (Online) DOI: 10.1007/BF02837397 Description: 32 pages, no figures.-- MSC1987 codes: 41A10, 46E35, 46G10.-- Part I of this paper published in: Acta Appl. Math. 80(3): 273-308 (2004), available at: http://e-archivo.uc3m.es/handle/10016/6482MR#: MR1928169 (2003h:42034)Zbl#: Zbl 1095.42014 Abstract: We present a definition of general Sobolev spaces with respect to arbitrary measures, $W k,p}(\Omega,\mu)$ for $1\leq p\leq\infty$. In Part I [Acta Appl. Math. 80(3): 273-308 (2004), http://e-archivo.uc3m.es/handle/10016/6482] we proved that these spaces are complete under very mild conditions. Now we prove that if we consider certain general types of measures, then $C infty_c({\bf R})$ is dense in these spaces. As an application to Sobolev orthogonal polynomials, we study the boundedness of the multiplication operator. This gives an estimation of the zeroes of Sobolev orthogonal polynomials. Sponsor: Research partially supported by a grant from DGES (MEC), Spain. Review: PeerReviewed Publisher version: http//dx.doi.org/10.1007/BF02837397 Keywords: Sobolev spaces with respect to measuresWeightsOrthogonal polynomialsCompleteness Rights: © Springer Appears in Collections: DM - GAMA - Artículos de Revistas