Hybrid Function Systems in the Theory of Uniform Distribution of Sequences

  • Peter Hellekalek
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 23)


A hybrid sequence in the multidimensional unit cube is a combination of two or more lower-dimensional sequences of different types. In this paper, we present tools to analyze the uniform distribution of such sequences. In particular, we introduce hybrid function systems, which are classes of functions that are composed of the trigonometric functions, the Walsh functions in base \(\mathbf{b}\), and the \(\mathbf{p}\)-adic functions. The latter are related to the dual group of the p-adic integers, p a prime. We prove the Weyl criterion for hybrid function systems and define a new notion of diaphony, the hybrid diaphony. Our approach generalizes several known concepts and results.



The author would like to thank Markus Neuhauser, NUHAG, University of Vienna, Austria, and RWTH Aachen, Germany, and Harald Niederreiter, University of Salzburg, and RICAM, Austrian Academy of Sciences, Linz, for several helpful comments.


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© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of SalzburgSalzburgAustria

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