Mean approximation of functions on the real axis by algebraic polynomials with Chebyshev-Hermite weight and widths of function classes

We obtain sharp Jackson-Stechkin type inequalities on the sets L (2,rho) (r) (a"e) 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,rho) (a"e). Also, for the classes , where r = 2, 3, h3, the exact values of the best polynomial approximations of the intermediate derivatives f ((nu)), nu = 1,..., r - 1, are obtained in L (2,rho) (R).