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Approximation theory for weighted Sobolev spaces on curves

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URI: https://hdl.handle.net/10016/6490
ISBN: 84-95301-56-3
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approximation_pestana_margarita_mathematica_2001.pdf (218.12 KB)
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2001
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Universidad de La Rioja
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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. We also prove the density of the polynomials in these spaces for non-closed compact curves and, finally, we find conditions under which the multiplication operator is bounded on the completion of polynomials. These results have applications to the study of zeroes and asymptotics of Sobolev orthogonal polynomials.
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17 pages, no figures.-- MSC2000 codes: 41A10, 46E35, 46G10.
MR#: MR1882649 (2003c:42002)
Keywords
Weighted Sobolev spaces, Polynomial approximation, Multiplication operator, Szegö theorem, Zeroes of orthogonal polynomials
Bibliographic citation
Margarita mathematica en memoria de José Javier (Chicho) Guadalupe Hernández (Luis Español y Juan L. Varona, eds), pp. 487-503
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