Geodesic
Bernstein's weighted approximation on $\Bbb R$ still has problems
Electronic transactions on numerical analysis, Tome 25 (2006), pp. 166-177.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: Let be continuous. Bernstein's approximation problem, posed in 1924, dealt with $\sterling $########$${\S}$$###$\copyright \ddot $§ approximation by polynomials in the norm ! " $\\%(' )102 ###$ # £$The qualitative form of this problem was solved by Achieser, Mergelyan, and Pollard, in the 1950's. Quantitative forms of the problem were actively investigated starting from the 1960's. We survey old and recent aspects of this topic. One recent finding is that there are weights for which the polynomials are dense, but which do not admit a Jackson-Favard inequality. In fact the weight exhibits this peculiarity. Moreover, not all $£3$54768#@9A{\S}BCEDGF 4HF 6 IQP spaces are the same when degree of approximation is considered. We also pose some open problems.$
Classification : 41A17
Keywords: weighted approximation, polynomial approximation, jackson-Bernstein theorems 
@article{ETNA_2006__25__a20,
     author = {Lubinsky, D.S.},
     title = {Bernstein's weighted approximation on $\Bbb R$ still has problems},
     journal = {Electronic transactions on numerical analysis},
     pages = {166--177},
     publisher = {mathdoc},
     volume = {25},
     year = {2006},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ETNA_2006__25__a20/}
}
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Lubinsky, D.S. Bernstein's weighted approximation on $\Bbb R$ still has problems. Electronic transactions on numerical analysis, Tome 25 (2006), pp. 166-177. http://geodesic.mathdoc.fr/item/ETNA_2006__25__a20/