Weighted Sobolev Spaces on Curves

descriptionPublicationkeyboard_double_arrow_right Article 01 Nov 2002 English Publisher:Elsevier BVJournal:Journal of Approximation Theory, volume 119, pages 41-85 (issn: 0021-9045,

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Authors: Venancio Alvarez; Domingo Pestana; José M. Rodríguez 0001; Elena Romera;

doi: 10.1006/jath.2002.3709

handle: 10016/6486

Weighted Sobolev Spaces on Curves

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Abstract

45 pages, no figures.-- MSC1987 codes: 41A10, 46E35, 46G10. MR#: MR1934626 (2003j:46038) Zbl#: Zbl 1019.46026 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. Research of second (D.P.), third (J.M.R.) and fourth (E.R.) authors was partially supported by a grant from DGI (BFM 2000-0206-C04-01), Spain. Publicado

Related Organizations

Carlos III University of Madrid
Spain
Carlos III University Madrid (UC3M)
Spain

Keywords

Mathematics(all), Numerical Analysis, Matemáticas, Applied Mathematics, density of polynomials, Sobolev space on a curve, Density of polynomials, multiplication operator, Multiplication operator, Sobolev spaces and other spaces of ``smooth'' functions, embedding theorems, trace theorems, Function spaces arising in harmonic analysis, Analysis

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