Geodesic
Sharp estimates for coefficients of odd trigonometric polynomials under a one-sided constraint
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 22 (2016) no. 3, pp. 130-136

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We study the largest and the smallest values of coefficients of odd trigonometric polynomials bounded from above by the function $\varphi(x)=x$ on the interval $[0,2\pi]$. A similar problem for the first and second coefficients was studied by the author earlier.
Keywords: trigonometric polynomials, one-sided constraints. 
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     title = {Sharp estimates for coefficients of odd trigonometric polynomials under a one-sided constraint},
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D. O. Zykov. Sharp estimates for coefficients of odd trigonometric polynomials under a one-sided constraint. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 22 (2016) no. 3, pp. 130-136. http://geodesic.mathdoc.fr/item/TIMM_2016_22_3_a11/