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Weierstrass' theorem in weighted Sobolev spaces with k derivatives: announcement of results

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URI: https://hdl.handle.net/10016/6453
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weierstrass_touris_etna_2006.pdf (110.96 KB)
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2006
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Kent State University
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Abstract
We characterize the set of functions which can be approximated by smooth functions and by polynomials with the norm $$ \ \ {W k,\infty}_w}=\sum_ {j=0} \ (j)}\ {L \infty}_{w_j}}, $$ for a wide range of (possibly unbounded) vector weights $w=(w_j's)$. We allow a great deal of independence among the weights $w=(w_j's)$.
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5 pages, no figures.-- MSC2000 codes: 41A10, 46E35, 46G10.
MR#: MR2219919 (2006m:41012)
Zbl#: Zbl 1107.41007
Keywords
Weierstrass' theorem, Weight, Sobolev spaces, Weighted Sobolev spaces
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Electronic Transactions in Numerical Analysis, 2006, vol. 24, p. 103-107
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