Geodesic
Mean Convergence of Hermite-Fejér Interpolation Based on the Zeros of Lascenov Polynomials
Canadian mathematical bulletin, Tome 39 (1996) no. 1, pp. 117-128

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DOI

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].
DOI : 10.4153/CMB-1996-016-3
Mots-clés : 41A05, Hermite-Fejér interpolation, mean convergence, orthogonal polynomials 
Shi, Ying Guang. Mean Convergence of Hermite-Fejér Interpolation Based on the Zeros of Lascenov Polynomials. Canadian mathematical bulletin, Tome 39 (1996) no. 1, pp. 117-128. doi: 10.4153/CMB-1996-016-3
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     author = {Shi, Ying Guang},
     title = {Mean {Convergence} of {Hermite-Fej\'er} {Interpolation} {Based} on the {Zeros} of {Lascenov} {Polynomials}},
     journal = {Canadian mathematical bulletin},
     pages = {117--128},
     year = {1996},
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     number = {1},
     doi = {10.4153/CMB-1996-016-3},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1996-016-3/}
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