On weighted Lebesgue function type sums |
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Authors: | Ying Guang Shi |
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Affiliation: | aDepartment of Mathematics, Hunan Normal University, Changsha, Hunan, China |
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Abstract: | Let I be a finite or infinite interval and dμ a measure on I. Assume that the weight function w(x)>0, w′(x) exists, and the function w′(x)/w(x) is non-increasing on I. Denote by ℓk's the fundamental polynomials of Lagrange interpolation on a set of nodes x1<x2<<xn in I. The weighted Lebesgue function type sum for 1≤i<j≤n and s≥1 is defined byIn this paper the exact lower bounds of Sn(x) on a “big set” of I and are obtained. Some applications are also given. |
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Keywords: | Weighted Lebesgue function type sum Lagrange interpolation Orthogonal polynomials |
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