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On the role of the Lebesgue functions in the theory of the Lagrange interpolation

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Literatur

  1. C denotes, as usual, the class of functions continuous for −1≦x≦+1.

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

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  3. S. Bernstein, Sur la limitation des valeurs etc.,Bull. Acad. Sc. De l'URSS,8 (1931), pp. 1025–1050.

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  4. L. Fejér, Lagrangesche Interpolation und die zugehörigen konjugierten Punkte,Math. Ann.,106 (1932), pp. 1–55.

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  5. Later onc 2,c 3,... denote generally also numerical constants. If somec v depends upon some parameters, the dependence will be explicitely stated.

  6. As usual, the class Lip γ denotes the totality of those functions which satisfy uniformly a Lipschitz-condition with the exponent γ in −1≦x≦+1.

  7. SeeS. N. Bernstein, Quelques remarques sur l'interpolation,Math. Ann.,79 (1918), pp. 1–12.

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  8. TheO-sign refers ton→∞ but always uniformly for −1≦x≦+1.

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Author information

Authors and Affiliations

  1. Jerusalem

    P. Erdős

  2. Budapest

    P. Turán (member of the Academy)

Authors
  1. P. Erdős
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  2. P. Turán
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Additional information

To Prof. dr.L. Fejér on the occasion of his 75th birthday

A part of the results (assertions a) and b) of this paper) was the subject of a lecture made by one of us at a colloquium for the constructive function-theory in Eger (Hungary), 29 Nov. 1953; they were found twenty years ago. The new results showing they are best possibles were a subject of another lecture in Pécs (Hungary), 18 Sept. 1954.

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Erdős, P., Turán, P. On the role of the Lebesgue functions in the theory of the Lagrange interpolation. Acta Mathematica Academiae Scientiarum Hungaricae 6, 47–66 (1955). https://doi.org/10.1007/BF02021267

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  • DOI: https://doi.org/10.1007/BF02021267

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