Certain properties of trigonometric series with monotone coefficients (Q1061333)

For functions f(x) that are sums of trigonometric series \(a_ 0/2+\sum^{\infty}_{\nu =1}a_ v \cos \nu x\) with coefficients satisfying the conditions \(a_{\nu}\to 0\) and \(\Delta_ ka_{\nu}\geq 0,\) one proves estimates for the smoothness moduli and best approximations in terms of the coefficients of this series.