Abstract
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 .
Acknowledgements
The authors thank the Deanship of Scientific Research – Jazan University for its support in financing this research project.