L∞ convergence of interpolation and associated product integration for exponential weights |
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Authors: | H S Jung |
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Institution: | Division of Applied Mathematics, KAIST, 373-1 Kusongdong, Yusongku, Taejon 305-701, South Korea |
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Abstract: | We investigate convergence in a weighted L∞ norm of Hermite–Fejér, Hermite, and Grünwald interpolations at zeros of orthogonal polynomials with respect to exponential weights such as Freud, Erd
s, and exponential weight on (−1,1). Convergence of product integration rules induced by the various approximation processes is deduced. We also give more precise weight conditions for convergence of interpolations with respect to above three types of weights, respectively. |
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Keywords: | Hermite Hermite– Fejé r Grü nwald interpolations Product integration rules Exponential weights |
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