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Einige Bemerkungen Über Stetige Funktionen Auf Topologischen Gruppen

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Part of the Lecture Notes in Mathematics book series (LNM,volume 1262)

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

  1. HWANG J.S., A problem on continuous and periodic functions, Pacific J. of Math. 117 (1985), 143–147.

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  2. HLAWKA E., Theorie der Gleichverteilung, Bibl. Inst., Mannheim-Wien-Zürich, 1979.

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  3. KUIPERS L. and NIEDERREITER H., Uniform Distribution of Sequences, John Wiley and Sons, New York, 1974.

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  4. 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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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-18015-9

  • Online ISBN: 978-3-540-47256-8

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