Geodesic
Sharp inequalities for trigonometric polynomials with respect to integral functionals
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 16 (2010) no. 4, pp. 38-53

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The problem on sharp inequalities for linear operators on the set of trigonometric polynomials with respect to integral functionals $\int_0^{2\pi}\varphi(|f(x)|)\,dx$ is discussed. A solution of the problem on trigonometric polynomials with given leading harmonic that deviate the least from zero with respect to such functionals over the set of all functions $\varphi$ determined, nonnegative, and nondecreasing on the semi-axis $[0,+\infty)$ is given.
Keywords: sharp inequalities for trigonometric polynomials, integral functional, trigonometric polynomials that deviate the least from zero. 
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     author = {V. V. Arestov},
     title = {Sharp inequalities for trigonometric polynomials with respect to integral functionals},
     journal = {Trudy Instituta matematiki i mehaniki},
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     url = {http://geodesic.mathdoc.fr/item/TIMM_2010_16_4_a3/}
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V. V. Arestov. Sharp inequalities for trigonometric polynomials with respect to integral functionals. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 16 (2010) no. 4, pp. 38-53. http://geodesic.mathdoc.fr/item/TIMM_2010_16_4_a3/