Burenkov, Victor and Almeida, G. E. G. 2006. Estimates of regularized solutions of integral equations of the first kind in anisotropic spaces with fractional orders of smoothness. Inverse Problems 22 (5) , pp. 1739-1759. 10.1088/0266-5611/22/5/013 |
Abstract
An integral equation of the first kind of convolution type is considered. A method closely related to Tikhonov regularization is used for constructing regularized approximate solutions that under certain assumptions converge to the exact solution of this ill-posed problem. V I Burenkov, I F Dorofeev and A S Pankratov obtained solutions of this problem for the isotropic case by using Nikol'skii-Besov spaces of functions possessing some common smoothness of fractional order as a means of characterizing the smoothness properties of the exact solution and the error on the right-hand side. The main aim of the present work is to obtain similar results for the anisotropic case, thus allowing the right-hand side error, the exact and regularized solutions to be considered as members of a wider class of functions than in the former case. A complete investigation of the anisotropic case is carried out. Some of the results obtained are also new for the isotropic case.
Item Type: | Article |
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Date Type: | Publication |
Status: | Published |
Schools: | Schools > Mathematics |
Subjects: | Q Science > QA Mathematics |
Uncontrolled Keywords: | Wavelet shrinkage; Besov-spaces |
Publisher: | Institute of Physics |
ISSN: | 0266-5611 |
Last Modified: | 04 Jun 2017 08:47 |
URI: | https://orca.cardiff.ac.uk/id/eprint/84913 |
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