Title: 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 , L 2 (R), L 2 β (R), which defined by the fractional derivatives of order β >0, have been considered in the space L 2 (R). The relation K ( f , t β , L 2 (R), L 2 β (R) ≈ ω β ( f, t ) ( t >0) was obtained in the sense of the weak equivalence, where ωω β ( f, t ) is the module of continuity of the fractional order β for a function f є L 2 (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.