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Gleichverteilte Doppelfolgen und eine Abschätzung der C-Diskrepanz

Uniformly distributed double sequences and an estimation of theC-discrepancy

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Abstract

In this paper a criterion forC-uniformly distributed differentiable functions is given by using uniformly distributed double sequences. This criterion allows to find lower bounds of theC-discrepancy of differentiable functions.

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Literatur

  1. Van Aardenne-Ehrenfest, T.: Proof of the impossibility of a just distribution of an infinite sequence of points over an interval. Indag. Math.7, 71–76 (1945).

    Google Scholar 

  2. Bergström, V.: Einige Bemerkungen zur Theorie der diophantischen Approximationen. Fysiogr. Sälsk. Lund. Förh.6, no. 13, 1–19 (1936).

    Google Scholar 

  3. Van Der Corput, J. G., undC. Pisot: Sur la discrépance modulo un. Indag. Math.1, 143–153 184–195, 260–269 (1939).

    Google Scholar 

  4. Erdös, P., undP. Turan: On a problem in the theory of uniform distribution I, II. Indag. Math.10, 370–378, 406–413 (1948).

    Google Scholar 

  5. Hlawka, E.: ÜberC-Gleichsverteilung. Ann. Mat. Pura Appl. (IV)49, 311–326 (1960).

    Google Scholar 

  6. Koksma, J. F.: Een algemeene stelling uit de theorie der gelijkmatige verdeeling modulo 1. Mathematica B (Zutphen)11, 7–11 (1942/43).

    Google Scholar 

  7. Roth, K. F.: On irregularities of distribution. Mathematika1, 73–79 (1954).

    Google Scholar 

  8. Schmidt, W. M.: Irregularities of distribution VII. Acta Arith.21, 45–50 (1972).

    Google Scholar 

  9. Kuipers, L., undH. Niederreiter: Uniform Distribution of Sequences. New York. J. Wiley & Sons. 1974.

    Google Scholar 

  10. Weyl, H.: Über die Gleichverteilung von Zahlen mod. Eins. Math. Ann.77, 313–352 (1916).

    Google Scholar 

  11. Kuipers, L.: Continuous and discrete distribution modulo 1. Indag. Math.15, 340–348 (1953).

    Google Scholar 

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Taschner, R.J. Gleichverteilte Doppelfolgen und eine Abschätzung der C-Diskrepanz. Monatshefte für Mathematik 88, 321–330 (1979). https://doi.org/10.1007/BF01534250

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  • DOI: https://doi.org/10.1007/BF01534250

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