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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Some inequalities for polynomials with a prescribed zero


Authors: Q. I. Rahman and G. Schmeisser
Journal: Trans. Amer. Math. Soc. 216 (1976), 91-103
MSC: Primary 30A04
MathSciNet review: 0399427
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Abstract: Let $ f(z)$ be a polynomial of degree n. Given that $ f(z)$ has a zero on the circle $ \vert z\vert = \rho \;(0 < \rho < \infty )$, we estimate $ \vert f(0)\vert$ and

$\displaystyle {({(2\pi )^{ - 1}}\int _0^{2\pi }\vert f({e^{i\theta }}){\vert^2}d\theta )^{1/2}}$

in terms of $ {\max _{\vert z\vert = 1}}\vert f(z)\vert$. We also consider some other related problems.

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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1976-0399427-7
PII: S 0002-9947(1976)0399427-7
Keywords: Polynomials with a prescribed zero, trigonometric polynomial, Chebyshev polynomial, entire function of exponential type
Article copyright: © Copyright 1976 American Mathematical Society