V V Kryzhniy 2003 Inverse Problems 19 1227 doi:10.1088/0266-5611/19/5/313
V V Kryzhniy
Show affiliationsThe paper describes a new method for building regularizing operators for the inversion of real-valued integral transforms. A one-parametric set of regularizing operators is built for each of the following integral transformations: Fourier sine and cosine, Hankel, Laplace and Meijer. The analytical link between the regularized and exact inverse integral transforms is common for all the integral transformations considered. It allows us to conduct a theoretical analysis that gives information about the rate of convergence, and reflects basic features of the numerical inversion of integral transforms. Features of the proposed method of implementation are illustrated with the help of numerical examples of Fourier sine and Laplace transformations.
42A38 Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type
Issue 5 (October 2003)
Received 13 May 2003, in final form 6 August 2003
Published 18 September 2003
V V Kryzhniy 2003 Inverse Problems 19 1227
M Nekipelov et al 2007 J. Phys. G: Nucl. Part. Phys. 34 627
H van Regemorter 1983 J. Phys. B: At. Mol. Phys. 16 L289
M Barma and R Ramaswamy 1986 J. Phys. A: Math. Gen. 19 L605
Lay Nam Chang and Chopin Soo 2003 Class. Quantum Grav. 20 1379
M M Akbar and Saurya Das 2004 Class. Quantum Grav. 21 1383
Z Silvestri et al 2003 Metrologia 40 172
P Malits and I D Vagner 1999 J. Phys. A: Math. Gen. 32 1507
Ramiz Hamid et al 2006 Metrologia 43 106
J M Collins et al 1991 Class. Quantum Grav. 8 L215