Estimates of regularized solutions of integral equations of the first kind in anisotropic spaces with fractional orders of smoothness.

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

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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
Date Type:	Publication
Status:	Published
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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