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

On the Hausdorff-limitability of {zn}

  • Wolfgang Luh


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.


Number Theory Algebraic Geometry Topological Group 
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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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