An inequality for the norm of a polynomial factor

Pritsker, Igor

doi:10.1090/S0002-9939-00-05818-4

An inequality for the norm of a polynomial factor
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by Igor E. Pritsker PDF

Proc. Amer. Math. Soc. 129 (2001), 2283-2291 Request permission

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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