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MAXIMUM MODULI OF UNIMODULAR POLYNOMIALS
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 Title & Authors
MAXIMUM MODULI OF UNIMODULAR POLYNOMIALS
Defant, Andreas; Garcia, Domingo; Maestre, Manuel;
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 Abstract
Let $\Sigma_{\alpha=m}\;s_{\alpha}z^{\alpha},\;z\;{\in}\;{\mathbb{C}}^n$ be a unimodular m-homogeneous polynomial in n variables (i.e. $s_{\alpha}\;=\;1$ for all multi indices ), and let be a (bounded complete) Reinhardt domain. We give lower bounds for the maximum modules $sup_{z\;{\in}\;R\;\Sigma_{\alpha=m}\;s_{\alpha}z^{\alpha}$, and upper estimates for the average of these maximum moduli taken over all possible m-homogeneous Bernoulli polynomials (i.e. for all multi indices ). Examples show that for a fixed degree m our estimates, for rather large classes of domains R, are asymptotically optimal in the dimension n.
 Keywords
several complex variables;power series;polynomials;Banach spaces;unconditional basis;Banach-Mazur distance;
 Language
English
 Cited by
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