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An inequality for the norm of a polynomial factor

Igor E. Pritsker
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Abstract

Let $p(z)$ be a monic polynomial of degree $n$, with complex coefficients, and let $q(z)$ be its monic factor. We prove an asymptotically sharp inequality of the form $\|q\|_{E} \le C^n \|p\|_E$, where $\|\cdot\|_E$ denotes the sup norm on a compact set $E$ in the plane. The best constant $C_E$ in this inequality is found by potential theoretic methods. We also consider applications of the general result to the cases of a disk and a segment.

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Igor E. Pritsker. 2000-01-24. An inequality for the norm of a polynomial factor. https://arxiv.org/abs/math/0001124

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