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Proceedings of the American Mathematical Society
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
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 $ \vert\vert p\vert\vert = (\int_{ - 1}^1 {\vert p(x){\vert^2}dx{)^{1/2}}} $. We determine sharp upper bounds for $ \vert{a_n}\vert/\vert\vert p\vert\vert$ and $ \vert{a_{n - 1}}\vert/\vert\vert p\vert\vert\;{\text{as}}\;p{\text{(x)}}\;{\text{: = }}\;\sum\nolimits_{\nu = 0}^n {{a_\nu }{x^\nu }} $ varies in $ {\mathcal{P}_n}$.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1987-0870788-8
PII: S 0002-9939(1987)0870788-8
Keywords: polynomials on the unit interval, coefficient estimates, Chebyshev polynomials, Legendre polynomials
Article copyright: © Copyright 1987 American Mathematical Society