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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Concerning polynomials on the unit interval
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by Q. M. Tariq PDF
Proc. Amer. Math. Soc. 99 (1987), 293-296 Request permission

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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Additional Information
  • © Copyright 1987 American Mathematical Society
  • 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