On the best mean square approximations by entire functions of exponential type in L 2(ℝ) and mean ν-widths of some functional classes

Abstract

We consider some extremal problems of approximation theory of functions on the whole real axis R by entire functions of the exponential type. In particular, we find the exact values of the mean ν-widths of classes of functions, defined by the modules of continuity of the mth order ω m and majorants Ψ satisfying the special type of restriction.