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The Weierstrass' approximation theorem for continuous functions on a compact space by using polynomials is well-known. As far as I know, there are some variants of this theorem, e.g. Stone-Weierstrass that refers not only to polynomials as approximator functions. Where could I find these Weierstrass-like approximation theorems? On-line references are OK, but one might also point to some books.

Thanks in advance, Lucian

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    Have you tried Wikipedia? It has a nice article on the Stone-Weierstrass theorem including some references, to Rudin's books among others, and they're really good books.2010-08-25
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    The book "Studies in Modern Analysis", Math. Assoc. America 1962, edited by McShane, has a paper by Stone himself called "A Generalized Weierstrass Approximation Theorem". According to a review of this book, this paper is a reprint (probably of Stone's 1948 paper in Math. Magazine, but I haven't checked that). Anyway, Stone explains in a leisurely way extensions of Weirestrass's classical theorem to several different settings and gives varied applications. Of course this reference is dated, but you can't go wrong by seeing what Stone had to say.2010-08-25

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