Geodesic
On an Extremal Problem in Fourier Series
Canadian mathematical bulletin, Tome 3 (1960) no. 2, p. 188

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Let f(x) be a bounded odd function, - π < x < π, |f(X)| ≤ 1, with non-negative Fourier coefficients bk, k = 1,2, ....Otto Szász [l] proved anew the existence of a bounded set of numbers {βn}, n = 1,2,..., such that where βn is the smallest constant satisfying the above inequality and added that 2/π ≤ βn ≤ 4/π. He pointed out [1, p. 170] that β1 = 4/π and raised the question of the value of βn for n > 1. 
Lorch, Lee. On an Extremal Problem in Fourier Series. Canadian mathematical bulletin, Tome 3 (1960) no. 2, p. 188. doi: 10.4153/CMB-1960-025-6
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[1] 1. Otto, Szász, Some extremum problems in the theory of Fourier series, Amer. J. of Math. 61 (1939), 165-177. Google Scholar

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