Stone-Weierstrass theorem

(redirected from Weierstrass approximation theorem)

Stone-Weierstrass theorem

[′stōn ′vī·ər‚sträs ‚thir·əm]
(mathematics)
If S is a collection of continuous real-valued functions on a compact space E, which contains the constant functions, and if for any pair of distinct points x and y in E there is a function ƒ in S such that ƒ(x) is not equal to ƒ(y), then for any continuous real-valued function g on E there is a sequence of functions, each of which can be expressed as a polynomial in the functions of S with real coefficients, that converges uniformly to g.
References in periodicals archive ?
n]f are known to give the most elegant proof of the Weierstrass approximation theorem for algebraic polynomials for the space C[0, 1], it is the Kantorovich polynomials [K.
Now, the Weierstrass approximation theorem yields the reconstruction of a function f 6 C[0, 1] as the limit for n [right arrow] [infinity of the sum (1.