Generalized weighted Sobolev spaces and applications to Sobolev orthogonal polynomials, II

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Show simple item record Rodríguez, José M. Romera, Elena Pestana, Domingo Álvarez, Venancio 2010-01-19T09:30:55Z 2010-01-19T09:30:55Z 2002-06
dc.identifier.bibliographicCitation Approximation Theory and its Applications, 2002, vol. 18, n. 2, p. 1-32
dc.identifier.issn 1000-9221 (Print)
dc.identifier.issn 1573-8175 (Online)
dc.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:
dc.description MR#: MR1928169 (2003h:42034)
dc.description Zbl#: Zbl 1095.42014
dc.description.abstract ^aWe 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),] 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.
dc.description.sponsorship Research partially supported by a grant from DGES (MEC), Spain.
dc.format.mimetype application/pdf
dc.language.iso eng
dc.publisher Springer
dc.rights © Springer
dc.subject.other Sobolev spaces with respect to measures
dc.subject.other Weights
dc.subject.other Orthogonal polynomials
dc.subject.other Completeness
dc.title Generalized weighted Sobolev spaces and applications to Sobolev orthogonal polynomials, II
dc.type article PeerReviewed
dc.description.status Publicado
dc.subject.eciencia Matemáticas
dc.identifier.doi 10.1007/BF02837397
dc.rights.accessRights openAccess
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