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Bivariate Polynomials of Least Deviation from Zero |
Canad. J. Math. 53(2001), 489-505
Published:2001-06-01
Printed: Jun 2001
Printed: Jun 2001
- Borislav D. Bojanov
- Werner Haußmann
- Geno P. Nikolov
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) |