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Zur Abschätzung der Fourier-Koeffizienten einer Funktion mit beschränkter Schwankung

An estimate of the fourier coefficients of a function of bounded variation

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Abstract

The Koksma-Hlawka inequality estimates the numerical integration error for a functionf of bounded variation in the sense of Hardy/Krause on thes-dimensional unit cube. The paper specifies an upper bound for the Vitali-variation of the functions obtained by holding given entries inf constant. This is applied to sharpen an estimate for the Fourier coefficients off, due to Zaremba.

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Literatur

  1. Hlawka, E.: Funktionen von beschränkter Variation in der Theorie der Gleichverteilung. Ann. Math. Pura Appl. (IV)54, 325–333 (1961).

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  2. Hlawka, E.: Zur angenäherten Berechnung mehrfacher Integrale. Mh. Math.66, 140–151 (1962).

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  3. Kuipers, L., Niederreiter, H.: Uniform Distribution of Sequences. New York: J. Wiley. 1974.

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  4. Zaremba, S. K.: La méthode des «bon treillis» pour le calcul numérique des intégrales multiples. In: Applications of Number Theory to Numerical Analysis. S. K. Zaremba (Ed.). pp. 39–119. New York: Academic Press. 1972.

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Authors and Affiliations

  1. Institut für Mathematik und Geometrie, Universität Innsbruck, Technikerstraße 13, A-6020, Innsbruck, Österreich

    Gilbert Helmberg

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  1. Gilbert Helmberg
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Herrn Professor E. Hlawka zum siebzigsten Geburtstag gewidmet

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Helmberg, G. Zur Abschätzung der Fourier-Koeffizienten einer Funktion mit beschränkter Schwankung. Monatshefte für Mathematik 102, 267–271 (1986). https://doi.org/10.1007/BF01304300

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  • DOI: https://doi.org/10.1007/BF01304300

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