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Miklos Schweitzer 1980_8

Source: Fourier series

January 28, 2009
functiontrigonometryreal analysisreal analysis unsolved

Problem Statement

Let f(x) f(x) be a nonnegative, integrable function on (0,2π) (0,2\pi) 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 n_k divides another. Prove that ∣ak∣≤a0 |a_k| \leq a_0. G. Halasz
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