MathDB

Given a positive integer

m

and

0 < \delta <\pi

, construct a trigonometric polynomial f(x)\equal{}a_0\plus{} \sum_{n\equal{}1}^m (a_n \cos nx\plus{}b_n \sin nx) of degree

m

such that f(0)\equal{}1, \int_{ \delta \leq |x| \leq \pi} |f(x)|dx \leq c/m, and \max_{\minus{}\pi \leq x \leq \pi}|f'(x)| \leq c/{\delta}, for some universal constant

c

. G. Halasz

Problem Statement