An inequality for trigonometric polynomials (Q2903923)

The purpose of the article is to prove 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 \(\xi \).