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Higher-Order Hermite-Fejér Interpolation for Stieltjes Polynomials

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  • Hee Sun Jung
  • Ryozi Sakai

Abstract

Let and be the ultraspherical polynomials with respect to . Then, we denote the Stieltjes polynomials with respect to satisfying . In this paper, we consider the higher-order Hermite-Fejér interpolation operator based on the zeros of and the higher order extended Hermite-Fejér interpolation operator based on the zeros of . When is even, we show that Lebesgue constants of these interpolation operators are and , respectively; that is, and . In the case of the Hermite-Fejér interpolation polynomials for , we can prove the weighted uniform convergence. In addition, when is odd, we will show that these interpolations diverge for a certain continuous function on , proving that Lebesgue constants of these interpolation operators are similar or greater than log .

Suggested Citation

  • Hee Sun Jung & Ryozi Sakai, 2013. "Higher-Order Hermite-Fejér Interpolation for Stieltjes Polynomials," Journal of Applied Mathematics, Hindawi, vol. 2013, pages 1-15, November.
    • Handle: RePEc:hin:jnljam:542653
    DOI: 10.1155/2013/542653
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