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.