On Hilbert extensions of Weierstrass' theorem with weights
In this paper we study the set of ℊ-valued functions which can be approximated by ℊ-valued continuous functions in the norm Lℊ∞(I,w), where I⊂ℝ is a compact interval, ℊ is a separable real Hilbert space and w is a certain ℊ-valued weakly measurable weight. Thus, we obtain a new extension of the cele...
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Hindawi Limited
2010-01-01
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| Series: | Journal of Function Spaces and Applications |
| Online Access: | http://dx.doi.org/10.1155/2010/645369 |
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doaj-fa99ace517fc442889144012ff3981662020-11-24T22:58:03ZengHindawi LimitedJournal of Function Spaces and Applications0972-68022010-01-018220121310.1155/2010/645369On Hilbert extensions of Weierstrass' theorem with weightsYamilet Quintana0Departamento de Matemáticas, Puras y Aplicadas, Edificio Matemáticas y Sistemas (MYS), Apartado Postal: 89000, Caracas 1080 A, Universidad Simón Bolívar, Caracas, VenezuelaIn this paper we study the set of ℊ-valued functions which can be approximated by ℊ-valued continuous functions in the norm Lℊ∞(I,w), where I⊂ℝ is a compact interval, ℊ is a separable real Hilbert space and w is a certain ℊ-valued weakly measurable weight. Thus, we obtain a new extension of the celebrated Weierstrass approximation theorem.http://dx.doi.org/10.1155/2010/645369 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Yamilet Quintana |
| spellingShingle |
Yamilet Quintana On Hilbert extensions of Weierstrass' theorem with weights Journal of Function Spaces and Applications |
| author_facet |
Yamilet Quintana |
| author_sort |
Yamilet Quintana |
| title |
On Hilbert extensions of Weierstrass' theorem with weights |
| title_short |
On Hilbert extensions of Weierstrass' theorem with weights |
| title_full |
On Hilbert extensions of Weierstrass' theorem with weights |
| title_fullStr |
On Hilbert extensions of Weierstrass' theorem with weights |
| title_full_unstemmed |
On Hilbert extensions of Weierstrass' theorem with weights |
| title_sort |
on hilbert extensions of weierstrass' theorem with weights |
| publisher |
Hindawi Limited |
| series |
Journal of Function Spaces and Applications |
| issn |
0972-6802 |
| publishDate |
2010-01-01 |
| description |
In this paper we study the set of ℊ-valued functions which can be approximated by ℊ-valued continuous functions in the norm Lℊ∞(I,w), where I⊂ℝ is a compact interval, ℊ is a separable real Hilbert space and w is a certain ℊ-valued weakly measurable weight. Thus, we obtain a new extension of the celebrated Weierstrass approximation theorem. |
| url |
http://dx.doi.org/10.1155/2010/645369 |
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AT yamiletquintana onhilbertextensionsofweierstrasstheoremwithweights |
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