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Weighted Weierstrass' theorem with first derivatives |
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| Authors: | Ana Portilla,Yamilet Quintana,Eva Tourí s |
| Affiliation: | a St. Louis University (Madrid Campus), Avenida del Valle 34, 28003 Madrid, Spain b Departamento de Matemáticas Puras y Aplicadas, Edificio Matemáticas y Sistemas (MYS), Universidad Simón Bolívar, Apartado Postal 89000, Caracas 1080 A, Venezuela c Departamento de Matemáticas, Escuela Politécnica Superior, Universidad Carlos III de Madrid, Avenida de la Universidad 30, 28911 Leganés, Madrid, Spain |
| Abstract: | We characterize the set of functions which can be approximated by continuous functions with the norm ‖f‖L∞(w) for every weight w. This fact allows to determine the closure of the space of polynomials in L∞(w) for every weight w with compact support. We characterize as well the set of functions which can be approximated by smooth functions with the norm ‖f‖W1,∞(w0,w1):=‖f‖L∞(w0)+‖f′‖L∞(w1), |
| Keywords: | Weierstrass' theorem Weight Sobolev spaces Weighted Sobolev spaces |
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