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Bivariate Polynomials of Least Deviation from Zero
Published online by Cambridge University Press: 20 November 2018
Abstract
Bivariate polynomials with a fixed leading term
${{x}^{m}}{{y}^{n}}$
, which deviate least from zero in the uniform or
${{L}^{2}}$-norm on the unit disk
$D$ (resp. a triangle) are given explicitly. A similar problem in
${{L}^{p}}$
,
$1\,\le \,p\,\le \,\infty $ is studied on
$D$ in the set of products of linear polynomials.
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- Copyright © Canadian Mathematical Society 2001
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