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Journal of Inverse and Ill-posed Problems

Editor-in-Chief: Kabanikhin, Sergey I.

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Volume 16, Issue 7 (Jan 2008)


Localization algorithms for singularities of solutions to convolution equations of the first kind

A. L. Ageev
  • Institute of Mathematics and Mechanics UrB RAS, Kovalevskaya st., 16, 620219 Ekaterinburg, Russia. Email:
/ T. V. Antonova
  • Institute of Mathematics and Mechanics UrB RAS, Kovalevskaya st., 16, 620219 Ekaterinburg, Russia. Email:
Published Online: 2008-11-21 | DOI: https://doi.org/10.1515/JIIP.2008.039


In this paper we construct and investigate localization algorithms for isolated singularities of a function which is a solution to a linear convolution equation of the first kind whose right-hand side is given with an error. We consider two types of singularities: δ-functions and discontinuities of the first kind. A problem for singularities localization is an ill-posed problem having perturbation. We use averaging methods defined by an averaging functional to obtain the singularities. We formulate conditions that the averaging functional must satisfy. For convolution equations, using the Fourier transform, we obtained upper estimates of precision of the singularities localization, separation threshold and other important characteristics of the supposed methods.

About the article

Received: 2008-02-02

Published Online: 2008-11-21

Published in Print: 2008-11-01

Citation Information: Journal of Inverse and Ill-posed Problems, ISSN (Online) 1569-3945, ISSN (Print) 0928-0219, DOI: https://doi.org/10.1515/JIIP.2008.039. Export Citation

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