An Inequality for Trigonometric Polynomials
Volume 60 / 2012
Bulletin Polish Acad. Sci. Math. 60 (2012), 241-247
MSC: 30D15, 41A17.
DOI: 10.4064/ba60-3-4
Abstract
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 $.
