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RISS 인기검색어
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- 저자 : Defant, (검색결과 2 건)
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MAXIMUM MODULI OF UNIMODULAR POLYNOMIALS
Defant, Andreas,Garcia, Domingo,Maestre, Manuel Korean Mathematical Society 2004 대한수학회지 Vol.41 No.1
Let $\Sigma_{$\mid$\alpha$\mid$=m}\;s_{\alpha}z^{\alpha},\;z\;{\in}\;{\mathbb{C}}^n$ be a unimodular m-homogeneous polynomial in n variables (i.e. $$\mid$s_{\alpha}$\mid$\;=\;1$ for all multi indices $\alpha$), and let $R\;{\subset}\;{\mathbb{C}}^n$ be a (bounded complete) Reinhardt domain. We give lower bounds for the maximum modules $sup_{z\;{\in}\;R\;$\mid$\Sigma_{$\mid$\alpha$\mid$=m}\;s_{\alpha}z^{\alpha}$\mid$$, and upper estimates for the average of these maximum moduli taken over all possible m-homogeneous Bernoulli polynomials (i.e. $s_{\alpha}\;=\;{\pm}1$ for all multi indices $\alpha$). Examples show that for a fixed degree m our estimates, for rather large classes of domains R, are asymptotically optimal in the dimension n.
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Maximum moduli of unimodular polynomials
Andreas Defant,Domingo Garc{\'\i}a,Manuel Maestre 대한수학회 2004 대한수학회지 Vol.41 No.1
Let |α|=m sαzα, z ∈ Cn be a unimodular m-homogeneous polynomial in n variables (i.e. |sα| = 1 for all multi indices α), and let R ⊂ Cn be a (bounded complete) Reinhardt domain. We give lower bounds for the maximum modulus supz∈R ||α|=msαzα|, and upper estimates for the average of these maximum moduli taken over all possible m-homogeneous Bernoulli polynomials (i.e. sα = ±1 for all multi indices α). Examples show that for a fixed degree m our estimates, for rather large classes of domains R, are asymptotically optimal in the dimension n.
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