Reverse Markov inequality

Norman Levenberg, Evgeny A. Poletsky

Research output: Contribution to journalArticle

11 Scopus citations

Abstract

Let K be a compact convex set in C. For each point zO ε ∂K and each holomorphic polynomial p = p(z) having all of its zeros in K, we prove that there exists a point z ε K with |z -zO| ≤ 20 diam K/ √deg p such that |p′(z)| ≥ (deg p)1/2/20(diam K) |p(zO)| i.e., we have a pointwise reverse Markov inequality. In particular, ∥p′∥k ≥ (deg p)1/2/20(diam K)∥p∥k.

Original languageEnglish (US)
Pages (from-to)173-182
Number of pages10
JournalAnnales Academiae Scientiarum Fennicae Mathematica
Volume27
Issue number1
StatePublished - Nov 1 2002

ASJC Scopus subject areas

  • Mathematics(all)

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