The Problem of A. F. Timan on the Precise Order of Decrease of the Best Approximations Original Research Article

The problem of Timan on finding a necessary and sufficient condition for Aσ(ƒ)Lq∼ωk(ƒ; 1/σ)Lq, σ → ∞, is solved. The condition is ωk(ƒ; δ)Lq ∼ ωk+1(ƒ; δ)Lq, δ → 0. Related problems in other situations have also been studied.