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Proceedings of the American Mathematical Society

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On pairs of coefficients of bounded polynomials


Authors: L. Brickman, Q. I. Rahman and St. Ruscheweyh
Journal: Proc. Amer. Math. Soc. 92 (1984), 533-537
MSC: Primary 30C10
MathSciNet review: 760940
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Abstract: Given a polynomial of degree at most $ n$, we estimate the sum of the moduli of any two of its coefficients in terms of its supremum norm on the unit disk.


References [Enhancements On Off] (What's this?)

  • [1] L. Brickman and St. Ruscheweyh, On bound preserving multipliers for $ H({\mathbf{D}})$ and applications to polynomials, preprint, 1983.
  • [2] H. P. Mulholland, On two extremum problems for polynomials on the unit circle, J. London Math. Soc. 31 (1956), 191–199. MR 0078504
  • [3] Q. I. Rahman, Inequalities concerning polynomials and trigonometric polynomials, J. Math. Anal. Appl. 6 (1963), 303–324. MR 0152796
  • [4] Otto Szász, Ungleichungen für die Koeffizienten einer Potenzreihe, Math. Z. 1 (1918), no. 2-3, 163–183 (German). MR 1544290, 10.1007/BF01203610

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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1984-0760940-1
Keywords: Bounded analytic functions, pairs of coefficients, polynomials
Article copyright: © Copyright 1984 American Mathematical Society