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Über eine Minimaleigenschaft der äquidistanten trigonometrischen Interpolation in 2n+1 Knoten

On a minimal property of the trigonometric interpolation at 2n+1 equidistant points

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Zusammenfassung

Wir betrachten das von Erdös gestellte Problem, das Integral über die Summe der Quadrate der Grundfunktionen der Lagrange-Interpolation durch trigonometrische Polynome an2n+1 Knoten zu minimieren.

Abstract

We consider the problem posed by Erdös of minimizing the sum of the squares of the fundamental functions of the Lagrange interpolation by trigonometric polynomials at2n+1 points.

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Literatur

  1. Bitzer, G.: Über Fragen der optimalen Lagrange-Interpolation. Dissertation, Bochum, 1974.

  2. Erdös, P.: Problems and results on the theory of interpolation II. Acta Math. Ac. Sci. Hung.12, 235–244 (1961).

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  4. Zygmund, A.: Trigonometric series, Bd. II. Cambridge: University Press 1959.

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Authors and Affiliations

  1. Fachbereich Mathematik, Universität Essen-Gesamthochschule, Universitätsstraße 2, D-4300, Essen 1, Bundesrepublik Deutschland

    G. Bitzer

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  1. G. Bitzer
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Bitzer, G. Über eine Minimaleigenschaft der äquidistanten trigonometrischen Interpolation in 2n+1 Knoten. Computing 21, 177–182 (1979). https://doi.org/10.1007/BF02253138

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  • DOI: https://doi.org/10.1007/BF02253138

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