Bernstein's weighted approximation on ℝ still has problems.
Lubinsky, D.S.
ETNA. Electronic Transactions on Numerical Analysis [electronic only], Tome 24 (2006), p. 166-177 / Harvested from The Electronic Library of Mathematics
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Publié le : 2006-01-01
EUDML-ID : urn:eudml:doc:127005 
@article{05134486,
     title = {Bernstein's weighted approximation on },
     journal = {ETNA. Electronic Transactions on Numerical Analysis [electronic only]},
     volume = {24},
     year = {2006},
     pages = {166-177},
     zbl = {1107.41013},
     language = {en},
     url = {http://dml.mathdoc.fr/item/05134486}
}

Lubinsky, D.S. Bernstein's weighted approximation on . ETNA. Electronic Transactions on Numerical Analysis [electronic only], Tome 24 (2006) pp. 166-177. http://gdmltest.u-ga.fr/item/05134486/