Pointwise strong approximation of almost periodic functions in S^1
We consider the class GM(2b) in pointwise estimate of the deviations in strong mean of S^1 almost periodic functions from matrix means of partial sums of their Fourier series.
Best approximation and moduli of smoothness: Computation and equivalence theorems
In this paper we investigate the trigonometric series with the @b-general monotone coefficients. First, we study the uniform convergence criterion. The estimates of best approximations and moduli of smoothness of the series in uniform metrics are obtained in terms of coefficients. These results imply several important relations between moduli of smoothness of different orders (in particular, Marchaud-type inequality) and best approximations.
Best Trigonometric Approximation, Fractional Order Derivatives and Lipschitz Classes
Let C 2π denote the space of 2π-periodic continuous functions and πn the set of trigonometric polynomials of degree ≦ n, where n ϵ P = {0, 1, … } . Given θ > 0, the well-known theorem of Stečkin and its converse state that the best approximation of an ƒ ϵ C 2π with respect to the max-norm satisfies