Citation:
Journal of Mathematical Analysis and Applications, 2007, vol. 334, n. 2, p. 1167-1198

ISSN:
0022-247X

DOI:
10.1016/j.jmaa.2006.12.066

Sponsor:
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.

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 suWe 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[+][-]

for a wide range of (even non-bounded) weights $w_0,w_1$. We allow a great deal of independence among the weights.for a wide range of (even non-bounded) weights $w_0,w_1$. We allow a great deal of independence among the weights.[+][-]

Description:

32 pages, no figures.-- MSC2000 codes: 41A10, 46E35, 46G10.