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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Concerning polynomials on the unit interval


Author: Q. M. Tariq
Journal: Proc. Amer. Math. Soc. 99 (1987), 293-296
MSC: Primary 26C05; Secondary 41A10
DOI: https://doi.org/10.1090/S0002-9939-1987-0870788-8
MathSciNet review: 870788
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Abstract: Let ${\mathcal {P}_n}$ be the normed linear space of all polynomials $p$ of degree $\leq n$ such that $p(1) = 0$ and $||p|| = (\int _{ - 1}^1 {|p(x){|^2}dx{)^{1/2}}}$. We determine sharp upper bounds for $|{a_n}|/||p||$ and $|{a_{n - 1}}|/||p||\;{\text {as}}\;p{\text {(x)}}\;{\text {: = }}\;\sum \nolimits _{\nu = 0}^n {{a_\nu }{x^\nu }}$ varies in ${\mathcal {P}_n}$.


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Keywords: polynomials on the unit interval, coefficient estimates, Chebyshev polynomials, Legendre polynomials
Article copyright: © Copyright 1987 American Mathematical Society