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
DOI:
https://doi.org/10.1090/S0002-9939-1984-0760940-1
MathSciNet review:
760940
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Abstract | References | Similar Articles | Additional Information
Abstract: Given a polynomial of degree at most 
, we estimate the sum of the moduli of any two of its coefficients in terms of its supremum norm on the unit disk.
- [1]
L. Brickman and St. Ruscheweyh, On bound preserving multipliers for
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, https://doi.org/10.1112/jlms/s1-31.2.191
- [3] Q. I. Rahman, Inequalities concerning polynomials and trigonometric polynomials, J. Math. Anal. Appl. 6 (1963), 303–324. MR 0152796, https://doi.org/10.1016/0022-247X(63)90011-8
- [4] Otto Szász, Ungleichungen für die Koeffizienten einer Potenzreihe, Math. Z. 1 (1918), no. 2-3, 163–183 (German). MR 1544290, https://doi.org/10.1007/BF01203610
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Additional Information
DOI:
https://doi.org/10.1090/S0002-9939-1984-0760940-1
Keywords:
Bounded analytic functions,
pairs of coefficients,
polynomials
Article copyright:
© Copyright 1984
American Mathematical Society