Downloads provided by UsageCountsWeighted Weierstrass' theorem with first derivatives
Copyright policy ) Portilla, Ana; Quintana, Yamilet; Rodríguez, José M.; Tourís, Eva;
Weighted Weierstrass' theorem with first derivatives
32 pages, no figures.-- MSC2000 codes: 41A10, 46E35, 46G10. MR#: MR2338656 (2008g:41004) Zbl#: Zbl pre05173014 We characterize the set of functions which can be approximated by continuous functions with the norm $\ \ {L infty(w)}$ for every weight w. This fact allows to determine the closure of the space of polynomials in $L infty(w)$ 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 $$ \ \ {W 1,\infty}(w_0,w_1)}\coloneq \ \ {L infty(w_0)}+ \ '\ {L infty(w_1)}, $$ for a wide range of (even non-bounded) weights $w_0,w_1$. We allow a great deal of independence among the weights. Research by first (A.P.), third (J.M.R.) and fourth (E.T.) autors was partially supported by three grants from MEC (MTM 2006-11976, MTM 2006-13000-C03-02, MTM 2006-26627-E), Spain. Publicado
- Simón Bolívar University Venezuela
- Carlos III University of Madrid Spain
- Escola Politècnica Superior d'Alcoi Spain
- Saint Louis University United States
- Saint Louis University Spain
Weierstrass' theorem, Matemáticas, Applied Mathematics, Sobolev spaces, Weighted Sobolev spaces, Sobolev spaces and other spaces of ``smooth'' functions, embedding theorems, trace theorems, Weight, approximation by smooth functions, Analysis, Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.), weighted spaces \(L^\infty\) and \(w^{1,\infty}\), approximation by polynomials
Weierstrass' theorem, Matemáticas, Applied Mathematics, Sobolev spaces, Weighted Sobolev spaces, Sobolev spaces and other spaces of ``smooth'' functions, embedding theorems, trace theorems, Weight, approximation by smooth functions, Analysis, Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.), weighted spaces \(L^\infty\) and \(w^{1,\infty}\), approximation by polynomials
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