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manuscripta mathematica

, Volume 7, Issue 4, pp 315–323 | Cite as

On the Hausdorff-limitability of {zn}

  • Wolfgang Luh
Article

Abstract

In this paper we are concerned with the Hausdorff-limitability of the sequence {zn}. Our aim is to solve a problem, which was posed by Agnew [1]. The Hx-transform of {zn}:
$$\sigma _n (z) = \int\limits_0^1 {\{ 1 + t(z - 1)\} ^n d\chi (t)}$$
(where: χ∈bv(0,1), χ(0)=χ(0+)=0, χ(1)=1) converges to the value zero for\(z \in r_r = \{ \varsigma :|\varsigma - (1 - \tfrac{1}{r})| = \tfrac{1}{r},\varsigma = |1\} (o< r \leqslant 1)\) if and only if χ satisfies the conditions: χ(t)=1 for t∈[r, 1] and χ is continuous at t=r.

Keywords

Number Theory Algebraic Geometry Topological Group 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

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Copyright information

© Springer-Verlag 1972

Authors and Affiliations

  • Wolfgang Luh
    • 1
  1. 1.Mathematisches Institut der UniversitätGießen

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