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Bivariate Polynomials of Least Deviation from Zero

Published:2001-06-01
Printed: Jun 2001
• Borislav D. Bojanov
• Werner Haußmann
• Geno P. Nikolov
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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.
 MSC Classifications: 41A10 - Approximation by polynomials {For approximation by trigonometric polynomials, see 42A10} 41A50 - Best approximation, Chebyshev systems 41A63 - Multidimensional problems (should also be assigned at least one other classification number in this section)

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