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Best Polynomial Approximation in Lp‐Norm and (p,q)‐Growth of Entire Functions

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  • Mohamed El Kadiri
  • Mohammed Harfaoui

Abstract

The classical growth has been characterized in terms of approximation errors for a continuous function on [−1,1] by Reddy (1970), and a compact K of positive capacity by Nguyen (1982) and Winiarski (1970) with respect to the maximum norm. The aim of this paper is to give the general growth ((p, q)‐growth) of entire functions in ℂn by means of the best polynomial approximation in terms of Lp‐norm, with respect to the set Ωr = {z ∈ Cn; exp VK(z) ≤ r}, where VK = sup {(1/d)log | Pd | , Pd polynomial of degree ≤ d, ∥Pd∥K ≤ 1} is the Siciak′s extremal function on an L‐regular nonpluripolar compact K is not pluripolar.

Suggested Citation

  • Mohamed El Kadiri & Mohammed Harfaoui, 2013. "Best Polynomial Approximation in Lp‐Norm and (p,q)‐Growth of Entire Functions," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    • Handle: RePEc:wly:jnlaaa:v:2013:y:2013:i:1:n:845146
    DOI: 10.1155/2013/845146
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    References listed on IDEAS

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    1. Mohammed Harfaoui, 2010. "Generalized Order and Best Approximation of Entire Function in ð ¿ ð ‘ -Norm," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2010, pages 1-15, January.
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