On Hilbert extensions of Weierstrass' theorem with weights

Details On Hilbert extensions of Weierstrass' theorem with weights On Hilbert extensions of Weierstrass' theorem with weights

2006-11-01

arxiv.org/abs/math/0611034v3

Mathematics

Classical Analysis and ODEs

Corrected version, 14 pages

Scientific paper

In this paper we study the set of functions $\GG$-valued which can be approximated by $\GG$-valued continuous functions in the norm $L^\infty_{\GG}(I,w)$, where $I$ is a compact interval, $\GG$ is a real and separable Hilbert space and $w$ is certain $\GG$-valued weakly measurable weight. Thus, we obtain a new extension of celebrated Weierstrass approximation theorem.

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