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

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URI: https://hdl.handle.net/10016/6482
ISSN: 0167-8019 (Print)
ISSN: 1572-9036 (Online)
DOI: 10.1023/B:ACAP.0000018790.82924.72
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generalized_pestana_aam_2004_ps.pdf (266.46 KB)
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2004-02
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Springer
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Abstract
In this paper we present a definition of Sobolev spaces with respect to general measures, prove some useful technical results, some of them generalizations of classical results with Lebesgue measure and find general conditions under which these spaces are complete. These results have important consequences in approximation theory. We also find conditions under which the evaluation operator is bounded.
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36 pages, no figures.-- MSC2000 codes: 41A10, 46E35, 46G10.-- Part II of this paper published in: Approx. Theory Appl. 18(2): 1-32 (2002), available at: http://e-archivo.uc3m.es/handle/10016/6483
MR#: MR2047389 (2005k:42062)
Zbl#: Zbl 1081.42024
Keywords
Sobolev spaces, Weights, Orthogonal polynomials
Bibliographic citation
Acta Applicandae Mathematicae, 2004, vol. 80, n. 3, p. 273-308
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