Abstract
The principal aim of this paper is to give an explicit construction for a sequence of polynomials that interpolates the function f on a given system of nodes and also converges to f uniformly. The functions we are able to approximate in this manner are continuous on the compact convex set K, and holomorphic in the interior of K.
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References
J.M. Anderson and J. G. Clunie: "Isomorphisms of the Disc Algebra and Inverse Faber sets" (to be published).
J.E. Andersson: Dissertation, Göteborg 1975.
T. Kövari and Ch. Pommerenke: "On Faber polynomials and Faber expansions", Math. Zeit., 99(1967), 193–206.
T. Kövari, "On the uniform approximation of analytic functions by means of interpolation polynomials”, Commentarii Math. Helv. 43(1968), 212–216.
T. Kövari and Ch. Pommerenke, "On the distribution of Fekete points", Mathematika, 15(1968), 70–75.
T. Kövari, "On the distribution of Fekete points II", Mathematika, 18(1971), 40–49.
T. Kövari, "On the order of polynomial approximation for closed Jordan domains", Journ. of Approx. Theory 5(1972), 362–373.
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© 1984 Springer-Verlag
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Kövari, T. (1984). On the uniform approximation of holomorphic functions on convex sets by means of interpolation polynomials. In: Graves-Morris, P.R., Saff, E.B., Varga, R.S. (eds) Rational Approximation and Interpolation. Lecture Notes in Mathematics, vol 1105. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0072416
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DOI: https://doi.org/10.1007/BFb0072416
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