BEST MEAN SQUARE APPROXIMATIONS BY ENTIRE FUNCTIONS OF FINITE DEGREE ON A STRAIGHT LINE AND EXACT VALUES OF MEAN WIDTHS OF FUNCTIONAL CLASSES

摘要

We obtain exact Jackson-type inequalities in the case of the best mean square approximation by entire functions of finite degree ≤ σ on a straight line. For classes of functions defined via majorants of averaged smoothness characteristics Ω1(f,t), t > 0, we determine the exact values of the Kolmogorov mean ν-width, linear mean ν-width, and Bernstein mean ν-width, ν > 0.