Publication:
Weighted Sobolev spaces on curves

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2002-11
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Elsevier
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Abstract
In this paper we present a definition of weighted Sobolev spaces on curves and find general conditions under which the spaces are complete for non-closed compact curves. We also prove the density of the polynomials in these spaces and, finally, we find conditions under which the multiplication operator is bounded in the space of polynomials.
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45 pages, no figures.-- MSC1987 codes: 41A10, 46E35, 46G10.
MR#: MR1934626 (2003j:46038)
Zbl#: Zbl 1019.46026
Keywords
Sobolev space on a curve, Density of polynomials, Multiplication operator
Bibliographic citation
Journal of Approximation Theory, 2002, vol. 119, n. 1, p. 41-85