An Inequality for Trigonometric Polynomials

摘要

The main result says in particular that if t(ζ):= ∑_(v=-n)~n c_ve~(ivζ) 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 c_n ≠ 0, then |t'(ξ)| ≥ μn for all real ξ.