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The highest smoothness of the Green function implies the highest density of a set

Vladimir V. Andrievskii Department of Mathematical Sciences, Kent State University

TBD mathscidoc:1701.333031

Arkiv for Matematik, 42, (2), 217-238, 2003.1
We investigate local properties of the Green function of the complement of a compact set$E$υ[0,1] with respect to the extended complex plane. We demonstrate, that if the Green function satisfies the 1/2-Hölder condition locally at the origin, then the density of$E$at 0, in terms of logarithmic capacity, is the same as that of the whole interval [0, 1]..
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@inproceedings{vladimir2003the,
  title={The highest smoothness of the Green function implies the highest density of a set},
  author={Vladimir V. Andrievskii},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203610987113840},
  booktitle={Arkiv for Matematik},
  volume={42},
  number={2},
  pages={217-238},
  year={2003},
}
Vladimir V. Andrievskii. The highest smoothness of the Green function implies the highest density of a set. 2003. Vol. 42. In Arkiv for Matematik. pp.217-238. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203610987113840.
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