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A converse of the Gauss--Lucas theorem

Complex Variables 2014-11-06 v1
Authors: Nikolai Nikolov , Blagovest Sendov
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Abstract

All linear operators L:C[z]→C[z]L:\mathcal{C}[z]\to \mathcal{C}[z] which decrease the diameter of the zero set of any P∈C[z]P\in\mathcal{C}[z] are found.

Keywords

Gauss-Lucas theorem converse linear operators zero set diameter

Cite

@article{arxiv.1307.8236,
  title  = {A converse of the Gauss--Lucas theorem},
  author = {Nikolai Nikolov and Blagovest Sendov},
  journal= {arXiv preprint arXiv:1307.8236},
  year   = {2014}
}

Comments

Amer. Math. Monthly (to appear in 2014)

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