Abstract
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.
The research of this author was supported, in part, by NSERC of Canada.
The research of this author was supported, in part, by NSF grant DMS-881-4026.
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© 1992 Springer-Verlag New York, Inc.
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Borwein, P., Saff, E.B. (1992). On the Denseness of Weighted Incomplete Approximations. In: Gonchar, A.A., Saff, E.B. (eds) Progress in Approximation Theory. Springer Series in Computational Mathematics, vol 19. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-2966-7_18
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DOI: https://doi.org/10.1007/978-1-4612-2966-7_18
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