Meansquare Approximation of Function Classes, Given on the all Real Axis R by the Entire Functions of Exponential Type

Abstract

K-functionals K (f, t, L2(R), L2β(R), which defined by the fractional derivatives of order β>0, have been considered in the space L2(R). The relation K (f, tβ, L2(R), L2β(R) ≈ ωβ (f, t) (t>0) was obtained in the sense of the weak equivalence, where ωωβ (f, t) is the module of continuity of the fractional order β for a function f є L2(R). Exact values of the best approximation by entire functions of exponential type v∏, v є (0, ∞) have been computed for the classes of functions, given by the indicated K-functionals and majorants Ψ satisfying specific restriction. Kolmogorov, Bernsteinand linear mean v-widths were obtained for indicated classes of functions.