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Mean Convergence of Hermite-Fejér Interpolation Based on the Zeros of Lascenov Polynomials
Ying Guang Shi
Journal:

Canadian Mathematical Bulletin / Volume 39 / Issue 1 / 01 March 1996

Published online by Cambridge University Press:

20 November 2018, pp. 117-128

Print publication:

01 March 1996
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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].

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