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

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URI: http://hdl.handle.net/10016/6483
ISSN: 1000-9221 (Print)
ISSN: 1573-8175 (Online)
DOI: 10.1007/BF02837397
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2002-06
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Springer
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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), 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.
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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/10016/6482
MR#: MR1928169 (2003h:42034)
Zbl#: Zbl 1095.42014
Keywords
Sobolev spaces with respect to measures, Weights, Orthogonal polynomials, Completeness
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Approximation Theory and its Applications, 2002, vol. 18, n. 2, p. 1-32
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