Convergence of Modified Lagrange Interpolation toLp-Functions Based on the Zeros of Orthonormal Polynomials with Freud Weights |
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| Authors: | R. Sakai |
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| Affiliation: | Department of Mathematics, Asuke Senior High School, Kawahara 5, Yagami, Asuke-cho, Higashikamo, Aichi, 444-2451, Japan |
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| Abstract: | We consider the “Freud weight”W2Q(x)=exp(−Q(x)). let 1<p<∞, and letL*n(f) be a modified Lagrange interpolation polynomial to a measurable functionf∈{f; ess supx∈ |f(x)| WQ(x)(1+|x|)α<∞},α>0. Then we have limn→∞ ∫∞−∞ [|f(x)−L*n(f; x)| WQ(x)(1+|x|)−Δ]p dx=0, whereΔis a constant depending onpandα. |
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