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A converse of the Gauss--Lucas theorem

preprint2013arXivOpen access
Nikolai NikolovBlagovest Sendov
math.CV
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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.

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