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On the maximum modulus principle for polynomials in a quasidisk
Authors:V V Andrievskii
Institution:(1) Department of Mathematical Sciences, Kent State University, 44242 Kent, OH, USA
Abstract:LetG⊂C be a quasidisk,K ⊂ G be a compact set, andp n be a non-constant complex polynomial of degree at mostn. We establish the inequality 
$$\mathop {\max }\limits_{z \in K} |p_n (z)| \leqslant (1 - \alpha )\mathop {\max }\limits_{z \in \partial G} |p_n (z)|,$$
whereα n < 0 depends onn, K, 
$$_{z \in \bar G} \left| {pn(z)} \right|$$
and the geometrical structure of ϖG.
Keywords:
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