Estimations of the best approximations of classes of infinitely differentiable functions in uniform and integral metrics

Original · EN

We find uniform with respect to parameter p (1≤ p≤∞) upper estimations of best approximations by trigonometric polynomials of classes Cψᵦ,ₚ of periodic functions generated by sequences ψ(k), that decrease to nought faster than any power function. Obtained estimations are exact for order and have constants that are written in explicit form and depend on function ψ only. We obtain analogical estimations for best approximations of classes Lψᵦ,₁ in metrics of spaces Lₛ, 1≤ s≤ ∞.