Widths of classes fromL 2[0, 2π] and minimization of exact constants in Jackson-type inequalities

Abstract

The problem of minimizing the constant in Jackson-type inequalities with respect to all subspaces of dimensionN, i.e., with respect to the entire set of approximating subspaces of dimensionN, is solved. It is shown that the constant in question is equal to the value of different widths of classL 2 (δ, τ, β, γ, θ).