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On the almost everywhere divergence of Lagrange interpolatory polynomials for arbitrary system of nodes

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References

  1. P. Erdős, Problems and results on the theory of interpolation. I,Acta Math. Acad. Sci. Hungar.,9 (1958), 381–388.

    Google Scholar 

  2. G. Faber, Über die interpolatorische Darstellung stetiger Funktionen,Jahresber. der Deutschen Math. Ver.,23 (1914), 190–210.

    Google Scholar 

  3. S. Bernstein, Sur la limitation des valeurs d'un polynome,Bull. Acad. Sci. de l'URSS,8 (1931), 1025–1050.

    Google Scholar 

  4. G. Grünwald, Über die Divergenzerscheinungen der Lagrangeschen Interpolationspolynome,Acta Sci. Math. Szeged,7 (1935), 207–221.

    Google Scholar 

  5. G. Grünwald, Über die Divergenzerscheinungen der Lagrangeschen Interpolationspolynome stetiger Funktionen,Annals of Math.,37 (1936), 908–918.

    Google Scholar 

  6. J. Marcinkiewicz, Sur la divergence des polynomes d'interpolation,Acta Sci. Math. Szeged,8 (1937), 131–135.

    Google Scholar 

  7. A. A. Privalov, divergence of Lagrange interpolation based on the Jacobi abscissas on sets of positive measure,Sibirsk. Mat., Z.,18 (1976), 837–859 (in Russian).

    Google Scholar 

  8. I. P. Natanson,Constructive Theory of Functions, GITTL (Moscow-Leningrad, 1949) (in Russian).

    Google Scholar 

  9. P. Turán, Some open problems of approximation theory,Mat. Lapok,25 (1974), 21–75 (in Hungarian).

    Google Scholar 

  10. P. Erdős andT. Grünwald, On polynomials with only real roots,Annals of Math.,40 (1939), 537–548.

    Google Scholar 

  11. P. Erdős andP. Turán, On interpolation. III,Annals of Math.,41 (1940), 510–553.

    Google Scholar 

  12. P. Erdős andJ. Szabados, On the integral of the Lebesgue function of interpolation,Acta Math. Acad. Sci. Hungar.,32 (1978), 191–195.

    Google Scholar 

  13. A. A. Privalov, Approximation of functions by interpolation polynomials, in “Fourier Analysis and Approximation Theory” I–II, North-Holland Publ. Co. (Amsterdam-Oxford-New York, 1978), 659–671.

    Google Scholar 

  14. S. N. Bernstein, Quelques remarques sur l'interpolation,Math. Ann.,79 (1918), 1–12.

    Article  Google Scholar 

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  1. Mathematical institute of the hungarian academy of sciences, Reáltanoda U. 13-15, 1053, Budapest

    P. Erdős (member of the Academy) & P. Vértesi

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  1. P. Erdős
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  2. P. Vértesi
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Dedicated to the memory of John Curtiss

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Erdős, P., Vértesi, P. On the almost everywhere divergence of Lagrange interpolatory polynomials for arbitrary system of nodes. Acta Mathematica Academiae Scientiarum Hungaricae 36, 71–89 (1980). https://doi.org/10.1007/BF01897094

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  • DOI: https://doi.org/10.1007/BF01897094

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