Hostname: page-component-848d4c4894-8kt4b Total loading time: 0 Render date: 2024-07-02T20:48:06.096Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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

1. Hermann, T., On Hermite-Fejèr interpolation, Acta Math. Hungar., 44(1984), 389–400.Google Scholar
2. Nevai, P., Orthogonal Polynomials, AMS Memoirs 213. Amer. Math. Soc., Providence, R.I. (1979).Google Scholar
3. Nevai, P. and Vértesi, P., Mean convergence of Hermit-Fejér interpolation, J. Math. Anal. Appl., 105(1985), 26–58.Google Scholar
4. Shi, Y.G., Some notes on Hermite-Fejèr type interpolation, Approx. Theory Appl., 7(1991), 28—39.Google Scholar
5. Turân, P., On some open problems of approximation theory, J. Approx. Theory, 29(1980), 23—85.Google Scholar
6. Vértesi, P., On some problems of P. Turân, Acta Math. Hungar., 29(1977), 337–353.Google Scholar
7. Vértesi, P., Hermite-Fejér type interpolations. II, Acta Math. Hungar., 33(1979), 333–343.Google Scholar
8. Vértesi, P., Hermite and Hermite-Fejér interpolations of higher order. II (mean convergence), Acta Math. Hungar., 56(1990), 369–380.Google Scholar
9. Vértesi, P. and Xu, Y., Mean convergence of quasi Hermite-Fejér interpolation, Studia Sci. Math. Hungar., 25(1990), 129–145.Google Scholar