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Bivariate Polynomials of Least Deviation from Zero

Published online by Cambridge University Press:  20 November 2018

Borislav D. Bojanov ,
Werner Haußmann  and
Geno P. Nikolov
Borislav D. Bojanov
Affiliation:
Department of Mathematics University of Sofia Boul. James Bourchier 5 1164 Sofia Bulgaria, email: [email protected]
Werner Haußmann
Affiliation:
Department of Mathematics Gerhard-Mercator-University Lotharstrasse 65 47048 Duisburg Germany, email: [email protected]
Geno P. Nikolov
Affiliation:
Department of Mathematics University of Sofia Boul. James Bourchier 5 1164 Sofia Bulgaria, email: [email protected]
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Abstract

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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.

Keywords

41A1041A5041A63
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 53 , Issue 3 , 01 June 2001 , pp. 489 - 505
Copyright
Copyright © Canadian Mathematical Society 2001

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