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Mean Convergence of Hermite-Fejér Interpolation Based on the Zeros of Lascenov Polynomials

Published online by Cambridge University Press:  20 November 2018

Ying Guang Shi
Ying Guang Shi*
Affiliation:
Institute of Computational Mathematical and Scientific/Engineering Computing, Chinese Academy of Sciences, P.O. Box 2719, Beijing, China 100080
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Abstract

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Weighted LP mean convergence of Hermite-Fejér interpolation based on the zeros of orthogonal polynomials with respect to the weight |x|2α+1(l — x2)β(α, β > — 1) is investigated. A necessary and sufficient condition for such convergence for all continuous functions is given. Meanwhile divergence of Hermite-Fejér interpolation in LP with p > 2 is obtained. This gives a possible answer to Problem 17 of P. Turân [J. Approx. Theory, 29(1980), p. 40].

Keywords

41A05Hermite-Fejér interpolationmean convergenceorthogonal polynomials
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 39 , Issue 1 , 01 March 1996 , pp. 117 - 128
Copyright
Copyright © Canadian Mathematical Society 1995

References

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