Displaying similar documents to “Positive trigonometric sums and applications.”

Integral presentations of deviations of de la Vallee Poussin right-angled sums

Vladimir I. Rukasov, Olga G. Rovenska (2009)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

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We investigate approximation properties of de la Vallee Poussin right-angled sums on the classes of periodic functions of several variables with a high smoothness. We obtain integral presentations of deviations of de la Vallee Poussin sums on the classes C β , ∞ m α .

An inequality for the coefficients of a cosine polynomial

Horst Alzer (1995)

Commentationes Mathematicae Universitatis Carolinae

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We prove: If 1 2 + ∑ k = 1 n a k ( n ) cos ( k x ) ≥ 0 for all x ∈ [ 0 , 2 π ) , then 1 - a k ( n ) ≥ 1 2 k 2 n 2 for k = 1 , ⋯ , n . The constant 1 / 2 is the best possible.