Widths in L2 of classes of differentiable functions, defined by higher-order moduli of continuity

Abstract

Sharp inequalities are obtained in the space L2, connecting the best approximations of differentiable 2π-periodic functions by trigonometric polynomials with integrals containing the higher-order moduli of continuity of the derivatives of these functions. The Kolmogorov widths of certain classes of functions, defined by these moduli of continuity, are computed.