Abstract
Some recent results of Hwang are generalized to compact topological groups. Furthermore a metric theorem for uniformly distributed sequences in a compact abelian group is proved. As a consequence, for every sequence \((b_n )_{n = 1}^\infty\) in a compact AA2-group G and every dense sequence \((x^n )_{n = 1}^\infty\) in G there exists a sequence (an) of integers with O≦an≦n such that \((x^{a_{n_{b_n } } } )\) is uniformly distributed in G.
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Literatur
HWANG J.S., A problem on continuous and periodic functions, Pacific J. of Math. 117 (1985), 143–147.
HLAWKA E., Theorie der Gleichverteilung, Bibl. Inst., Mannheim-Wien-Zürich, 1979.
KUIPERS L. and NIEDERREITER H., Uniform Distribution of Sequences, John Wiley and Sons, New York, 1974.
TICHY R.F. and TURNWALD G., On the discrepancy of some special sequences, Journal of Number Theory, im Druck.
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© 1987 Springer-Verlag
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Tichy, R.F. (1987). Einige Bemerkungen Über Stetige Funktionen Auf Topologischen Gruppen. In: Hlawka, E. (eds) Zahlentheoretische Analysis II. Lecture Notes in Mathematics, vol 1262. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0078603
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DOI: https://doi.org/10.1007/BFb0078603
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