Order estimates for best approximations and moduli of continuity of the sum of a trigonometric series with quasi-monotone coefficients
For two classes of \(2 \pi\)-periodic functions with nonnegative Fourier coefficients \(a_ n\) such that \(a_ n n^{-\theta} \geq a_{n+1} (n+1)^{-\theta}\) \((\theta \geq 0)\) and \(\sum a_ n<\infty\) and, respectively, \(n a_ n \to 0\) as \(n \to \infty\), the author obtains order of best approximations and of the moduli of continuity.
scientific article; zbMATH DE number 484293