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Generalized weighted Sobolev spaces and applications to Sobolev orthogonal polynomials: a survey

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2006
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Kent State University
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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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6 pages, no figures.-- MSC2000 codes: 41A10, 46E35, 46G10.
MR#: MR2219917 (2006k:42051)
Zbl#: Zbl 1146.42005
Keywords
Sobolev spaces, Weights, Orthogonal polynomials
Bibliographic citation
Electronic Transactions on Numerical Analysis, 2006, vol. 24, p. 88-93