Let f(x) be a nonnegative, integrable function on (0,2π) whose Fourier series is f(x)\equal{}a_0\plus{}\sum_{k\equal{}1}^{\infty} a_k \cos (n_k x), where none of the positive integers nk divides another. Prove that ∣ak∣≤a0.
G. Halasz functiontrigonometryreal analysisreal analysis unsolved