Journal of Advances in Applied Mathematics

Download PDF (199.5 KB) PP. 146 - 158 Pub. Date: October 6, 2020

DOI: 10.22606/jaam.2020.54002

• Ryozi SAKAI^*
  Department of Mathematics, Meijo University, Tenpaku-ku Nagoya 468-8502, Japan

Let R = (−∞,∞), and let Q ∈ C^1(R) : R → [0,∞) be an even function which is an exponent. We consider the weight w(x) = e^−Q(x), x ∈ R and then we can construct the orthonormal polynomials pn(w^2; x) of degree n for w^2(x). In this paper, we study the (l, ν) order Hermite-Fej´er interpolation polynomial Ln(l, ν, f; x) based on the zeros {xk,n}n^k =1 of pn(w^2; x), and we estimate the Lebesgue function of Ln(l, ν, f; x).

higher order Hermite-Fej´er interpolation polynomial, Lebesgue function

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