General discrepancy estimates III: The Erdös-Turán-Koksma inequality for the Haar function system |
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Authors: | Peter Hellekalek |
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Affiliation: | (1) Institut für Mathematik, Universität Salzburg, Hellbrunner Strasse 34, A-5020 Salzburg, Austria |
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Abstract: | The classical Erdös-Turán-Koksma inequality gives us an upper bound for the discrepancy of a sequence in thes-dimensional unit cube in terms of exponential sums, more precisely, in terms of the trigonometric function system.In this paper, we shall prove the inequality of Erdös-Turán-Koksma for the extreme and the star discrepancy, for generalized Haar function systems. Further, we shall show the existence of the inequality of Erdös-Turán-Koksma for the isotropic discrepancy, for generalized Haar and Walsh function systems.Research supported by the Austrian Science Foundation, project no. P9285/TEC. |
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Keywords: | 11K06 11K38 65C05 65C10 |
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