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Belov, A. S.
Proceedings of the Steklov Institute of Mathematics, 12/2022, Letnik: 319, Številka: 1Journal Article, Conference Proceeding
We prove that for each positive integer the conjugate Dirichlet kernel is semiadditive on the interval , that is, for any nonnegative real numbers and such that ; moreover, for positive and with , the equality is attained if and only if the condition is satisfied. We use this property of the conjugate Dirichlet kernel to study the sum of a sine series with monotone coefficients. We also examine the properties of some nonnegative trigonometric polynomials.
