Order estimations of the best approximations and approximations of the Fourier sums on the classes of infinitely differentiable functions

الأصل · EN

We obtained order estimations for the best uniform approximations by trigonometric polynomials and approximations by Fourier sums of classes of 2π-periodic continuous functions, which (ψ,β)-derivatives fβψ belong to unit balls of spaces Lₚ, 1≤ p<∞ in case at consequences ψ(k) decrease to nought faster than any power function. We also established the analogical estimations in Lₛ-metric, 1<s≤∞, for classes of the summable (ψ,β)-differentiable functions, such that ∥ fβψ∥₁≤1.