ON SOME EXTREMAL PROBLEMS OF THE BEST APPROXIMATION BY ENTIRE FUNCTIONS
In this paper a number of extremal problems of approximation theory of square summable functions on the whole line R : = (-∞, +∞) by entire functions of exponential type. In the space L 2(R) of the exact constants of Jackson- Stechkin type inequalities were calculated. Found There was found the upper bounds approximation of classes of functions L 2(R), defined with the help of the average modulus of continuity of m-th order, where instead of the shiftoperator Th ( f, x ): = f ( x + h ) is used Steklov’s operator Sh ( f ).Similar smoothness characteristics for solving the extremal problems of approximation theory for periodicfunctions in L 2[0,2 π ] were previously considered in the works by V. A. Abilov, F. I. Abilova, S. B. Vakarchuk, M. Sh. Shabozov and others. It is proved that the obtained results in this paper are ultimate does not approving.