On discrete analogues of fractional smoothness functions (Q1382586)

The author introduces a discrete analogue of the class of fractional smoothness functions. It is shown that this class contains the natural discrete approximation for each function of the initial ``continuous'' class. For the introduced classes the order estimates of minimal 1-approximating sets are found and a synthesis method is proposed for functional element schemes realizing discrete functions with error not larger than 1 of small order and with complexity close to the minimal possible one.