Abstract
We study the Fourier multiplier operators , where be a bounded function; and we establish for them uncertainty principle of concentration type for the Donoho-Stark's case. Next, we give an application of the general theory of reproducing kernels to the Tikhonov regularization for . Meanwhile, we give the approximate formulas for on the Sobolev spaces. Further, we shall establish error estimates for our approximation formulas; and we examine convergence rates of these type of approximations. Finally, by using computers, we shall illustrate numerical experiments approximation formulas for the partial sum operator in the two dimensions.