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Transactions of the American Mathematical Society

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



Location of the zeros of polynomials with a prescribed norm

Authors: Q. I. Rahman and G. Schmeisser
Journal: Trans. Amer. Math. Soc. 196 (1974), 69-78
MSC: Primary 30A06
MathSciNet review: 0349968
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Abstract: For monic polynomials $ {f_n}(z)$ of degree n with prescribed $ {L^p}$ norm $ (1 \leq p \leq \infty )$ on the unit circle or supremum norm on the unit interval we determine bounded regions in the complex plane containing at least $ k(1 \leq k \leq n)$ zeros. We deduce our results from some new inequalities which are similar to an inequality of Vicente Gonçalves and relate the zeros of a polynomial to its norm.

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Keywords: Location of zeros, inequalities for polynomials, best approximation by polynomials, extremal problems
Article copyright: © Copyright 1974 American Mathematical Society

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