Analytical and numerical applications for the Fourier multiplier operators on ℝⁿ × (0, ∞)

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 .

Keywords:

• Fourier multiplier operators
• Heisenberg–Pauli–Weyl uncertainty principle
• concentration uncertainty principle
• Tikhonov regularization
• approximate formulas
• Gauss–Kronrod method
• numerical experiments

AMS Subject Classifications:

• 42B10
• 42B15
• 46E35

Acknowledgements

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