Analytical and numerical applications for the Fourier multiplier operators on Double-struck capital Rn x (0, ∞)

We study the Fourier multiplier operators , where and ; and we establish for them some versions of uncertainty principles. Moreover, we give an application of the general theory of reproducing kernels to the Tikhonov regularization for . Meanwhile, we give the approximate formulas for on a Hilbert space . Further, we shall establish error estimates for our approximation formulas. Finally, by using computers, we shall illustrate numerical experiments approximation formulas in .