An Inequality for Trigonometric Polynomials

@article{N2012,
abstract = {The main result says in particular that if $t(ζ):= ∑_\{ν=-n\}ⁿ c_ν e^\{iνζ\}$ is a trigonometric polynomial of degree n having all its zeros in the open upper half-plane such that |t(ξ)| ≥ μ on the real axis and cₙ ≠ 0, then |t’(ξ)| ≥ μn for all real ξ.},
author = {N. K. Govil, Mohammed A. Qazi, Qazi I. Rahman},
journal = {Bulletin of the Polish Academy of Sciences. Mathematics},
keywords = {polynomials; Laurent polynomial; Bernstein's inequality; minimum modulus},
language = {eng},
number = {3},
pages = {241-247},
title = {An Inequality for Trigonometric Polynomials},
url = {http://eudml.org/doc/281159},
volume = {60},
year = {2012},
}

TY - JOUR
AU - N. K. Govil
AU - Mohammed A. Qazi
AU - Qazi I. Rahman
TI - An Inequality for Trigonometric Polynomials
JO - Bulletin of the Polish Academy of Sciences. Mathematics
PY - 2012
VL - 60
IS - 3
SP - 241
EP - 247
AB - The main result says in particular that if $t(ζ):= ∑_{ν=-n}ⁿ c_ν e^{iνζ}$ is a trigonometric polynomial of degree n having all its zeros in the open upper half-plane such that |t(ξ)| ≥ μ on the real axis and cₙ ≠ 0, then |t’(ξ)| ≥ μn for all real ξ.
LA - eng
KW - polynomials; Laurent polynomial; Bernstein's inequality; minimum modulus
UR - http://eudml.org/doc/281159
ER -