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Journal of Advances in Applied Mathematics
JAAM > Volume 5, Number 4, October 2020

Lebesgue Function for Higher Order Hermite-Fej´er Interpolation Polynomials with Exponential-Type Weights

Download PDF  (199.5 KB)PP. 146-158,  Pub. Date:October 9, 2020
DOI: 10.22606/jaam.2020.54002

Author(s)
Ryozi SAKAI
Affiliation(s)
Department of Mathematics, Meijo University, Tenpaku-ku Nagoya 468-8502, Japan
Abstract
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).
Keywords
higher order Hermite-Fej´er interpolation polynomial, Lebesgue function
References
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