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An Inequality for Trigonometric Polynomials

Volume 60 / 2012

N. K. Govil, Mohammed A. Qazi, Qazi I. Rahman Bulletin Polish Acad. Sci. Math. 60 (2012), 241-247 MSC: 30D15, 41A17. DOI: 10.4064/ba60-3-4


The main result says in particular that if $t (\zeta ) := \sum _{\nu = -n}^n c_\nu e^{ i \nu \zeta }$ is a trigonometric polynomial of degree $n$ having all its zeros in the open upper half-plane such that $|t (\xi )| \geq \mu $ on the real axis and $c_n \not = 0$, then $|t^\prime (\xi )| \geq \mu n$ for all real $\xi $.


  • N. K. GovilDepartment of Mathematics
    Auburn University
    Auburn, AL 36849-5310, U.S.A.
  • Mohammed A. QaziDepartment of Mathematics
    Tuskegee University
    Tuskegee, AL 36088, U.S.A.
  • Qazi I. RahmanDépartement de Mathématiques et de Statistique
    Université de Montréal
    Montréal, H3C 3J7, Canada

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