Geodesic
Coefficients of trigonometric polynomials under a one-sided constraint
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 21 (2015) no. 4, pp. 152-160

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For odd trigonometric polynomials bounded from above by the function $\varphi(x)=x$ on the intervals $[0, \pi]$ and $[0, 2 \pi]$, we study the maximum and minimum values of coefficients. We obtain two-sided estimates for the first coefficient and find the asymptotic behavior of its maximum and minimum values with respect to the order of the polynomial. We estimate the leading coefficients.
Keywords: trigonometric polynomial, one-sided constraints. 
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     author = {D. O. Zykov},
     title = {Coefficients of trigonometric polynomials under a one-sided constraint},
     journal = {Trudy Instituta matematiki i mehaniki},
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     url = {http://geodesic.mathdoc.fr/item/TIMM_2015_21_4_a14/}
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D. O. Zykov. Coefficients of trigonometric polynomials under a one-sided constraint. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 21 (2015) no. 4, pp. 152-160. http://geodesic.mathdoc.fr/item/TIMM_2015_21_4_a14/