Mean Approximation of Functions on the Real Axis by Algebraic Polynomials with Chebyshev-Hermite Weight and Widths of Function Classes

摘要

We obtain sharp Jackson-Stechkin type inequalities on the sets L_(2,ρ)~r(R) in which the values of best polynomial approximations are estimated from above via both the moduli of continuity of mth order and K-functionals of rth derivatives. For function classes defined by these characteristics, the exact values of various widths are calculated in the space L_(2,ρ)(R). Also, for the classes W_(2,ρ)~r(K_m,Ψ), where r = 2,3,..., the exact values of the best polynomial approximations of the intermediate derivatives f~((v)), v = 1,..., r - 1, are obtained in L_(2,ρ)(R).