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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Homogeneous polynomials on the ball of $ {\bf C}\sp 2$


Author: Josip Globevnik
Journal: Proc. Amer. Math. Soc. 103 (1988), 255-259
MSC: Primary 32H35; Secondary 32E10
MathSciNet review: 938679
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Abstract: Let $ {B_2}$ be the open unit ball of $ {C^2}$. Let $ T = \left\{ {\left( {u,w} \right) \in b{B_2}:1 - a \leq {{\left\vert u \right\vert}^2} \leq a} \right.$ where $ 1/2 < a < 1/2 + \sqrt 3 /4$. For each $ n \in {\mathbf{N}}$ we construct a homogeneous polynomial $ {H_n}:{C^2} \to {C^2}$ of degree $ n$ such that $ \left\vert {{H_n}} \right\vert \leq 1$ on $ {B_2}$ and $ \left\vert {{H_n}} \right\vert \geq c$ on $ T$ where $ c > 0$ does not depend on $ n$.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1988-0938679-2
PII: S 0002-9939(1988)0938679-2
Article copyright: © Copyright 1988 American Mathematical Society