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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48 .

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Inequalities for polynomials with a prescribed zero
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by A. Giroux and Q. I. Rahman PDF
Trans. Amer. Math. Soc. 193 (1974), 67-98 Request permission

Abstract:

Inequalities for the derivative and for the maximum modulus on a larger circle of a polynomial with a given zero on the unit circle are obtained in terms of its degree and maximum modulus on the unit circle; examples are given to show that these are sharp with respect to the degree (best constants are not known). Inequalities for ${L^p}$ norms, in particular ${L^2}$ norms, are also derived. Also certain functions of exponential type are considered and similar inequalities are obtained for them. Finally, the problem of estimating ${P_n}(r)$ (with $0 < r < 1$) given ${P_n}(1) = 0$ is taken up.
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Additional Information
  • © Copyright 1974 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 193 (1974), 67-98
  • MSC: Primary 30A06
  • DOI: https://doi.org/10.1090/S0002-9947-1974-0352427-3
  • MathSciNet review: 0352427