On the Denseness of Weighted Incomplete Approximations
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For a given weight function w(x) on an interval [a, b], we study the generalized Weierstrass problem of determining the class of functions f ∈ C[a, b] that are uniform limits of weighted polynomials of the form w n (x)p n (x) 1 ∞ , where p n is a polynomial of degree at most n. For a special class of weights, we show that the problem can be solved by knowing the denseness interval of the alternation points for the associated Chebyshev polynomials.
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