Approximation by polynomials and smooth functions in Sobolev spaces with respect to measures

Authors:
José M. Rodríguez
Affiliations:
Departamento de Matemáticas, Escuela Politécnica Superior, Universidad Carlos III de Madrid, Avenida de la Universidad, 30 28911 Leganés, Madrid, Spain
Venue:
Journal of Approximation Theory
Year:
2003

Citing 4
Cited 2

Orthogonal polynomials and approximation in Sobolev spaces

VII SPOA Proceedings of the seventh Spanish symposium on Orthogonal polynomials and applications
Zero location and nth asymptotics of Sobolev orthogonal polynomials

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Weierstrass' theorem in weighted Sobolev spaces

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The multiplication operator in Sobolev spaces with respect to measures

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Weierstrass' theorem with weights

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A simple characterization of weighted Sobolev spaces with bounded multiplication operator

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Abstract

The density of polynomials is straightforward to prove in Sobolev spaces Wk,p((a, b)), but there exist only partial results in weighted Sobolev spaces; here we improve some of these theorems. The situation is more complicated in infinite intervals, even for weighted LP spaces; besides, in the present paper we have proved some other results for weighted Sobolev spaces in infinite intervals.