Fethi Soltani and Adel Almarashi and Idir Mechai
Numerical Applications of Tikhonov Regularization for the Fourier Multiplier Operators
130 - 142
2016
10
3
International Journal of Mathematical and Computational Sciences
https://publications.waset.org/pdf/10004459
https://publications.waset.org/vol/111
World Academy of Science, Engineering and Technology
Tikhonov regularization and reproducing kernels are the
most popular approaches to solve illposed problems in computational
mathematics and applications. And the Fourier multiplier operators
are an essential tool to extend some known linear transforms
in Euclidean Fourier analysis, as Weierstrass transform, Poisson
integral, Hilbert transform, Riesz transforms, BochnerRiesz mean
operators, partial Fourier integral, Riesz potential, Bessel potential,
etc. Using the theory of reproducing kernels, we construct a simple
and efficient representations for some class of Fourier multiplier
operators Tm on the PaleyWiener space Hh. In addition, we give
an error estimate formula for the approximation and obtain some
convergence results as the parameters and the independent variables
approaches zero. Furthermore, using numerical quadrature integration
rules to compute single and multiple integrals, we give numerical
examples and we write explicitly the extremal function and the
corresponding Fourier multiplier operators.
Open Science Index 111, 2016