Bivariate Polynomials of Least Deviation from Zero
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 produc...
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| Veröffentlicht in: | Canadian journal of mathematics 2001-06, Vol.53 (3), p.489-505 |
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| Hauptverfasser: | , , |
| Format: | Artikel |
| Sprache: | eng |
| Online-Zugang: | Volltext |
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| Zusammenfassung: | 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. |
|---|---|
| ISSN: | 0008-414X 1496-4279 |
| DOI: | 10.4153/CJM-2001-021-3 |