Dinh Dung and Mai Xuan Thao

Abstract

     We study the optimal recovery of multivariate periodic functions of the Besov class of common smoothness SB^w_p,q  from their values at  n points in terms of the quantity R_n(SB^w_p,q ,L_q), which is a characterization of optimality of methods of recovery. The smoothness of SB^w_p,q  is defined via modulus of smoothness dominated by a function w  of modulus of smoothness type. With some restrictions on w and p, q we give the asymptotic order of this quantity when n ---> ¥ . An asymptotically optimal method of recovery is constructed by using the wavelet family formed from the integer translates of the dyadic scales of multivariate de la Vallée Poussin kernels.