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Journal of Inverse and Ill-posed Problems

Editor-in-Chief: Kabanikhin, Sergey I.

6 Issues per year


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1569-3945
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Volume 16, Issue 6 (Jan 2008)

Issues

Modulus of continuity for conditionally stable ill-posed problems in Hilbert space

B. Hofmann
  • Department of Mathematics, Chemnitz University of Technology, 09107 Chemnitz, Germany. Email:
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
/ P. Mathé
  • Weierstraß Institute for Applied Analysis and Stochastics, Mohrenstraße 39, 10117 Berlin, Germany. Email:
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
/ M. Schieck
  • Department of Mathematics, Chemnitz University of Technology, 09107 Chemnitz, Germany. Email:
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
Published Online: 2008-09-30 | DOI: https://doi.org/10.1515/JIIP.2008.030

Abstract

One of the fundamental results in the theory of ill-posed inverse problems asserts that these problems can become conditionally well-posed when restricting the domain of the forward operator in an appropriate manner. This leads to the study of certain moduli of continuity for the associated restricted inverse operator. The authors systematically study this modulus of continuity and highlight its intimate connection to error bounds of various regularizing procedures. The contributions of V. K. Ivanov and his concept of quasi-solutions are fundamental for such analysis.

Key words.: Linear ill-posed problems; conditional stability; modulus of continuity; quasi-solution; regularization; error estimates

About the article

Received: 2008-04-11

Published Online: 2008-09-30

Published in Print: 2008-10-01


Citation Information: Journal of Inverse and Ill-posed Problems, ISSN (Online) 1569-3945, ISSN (Print) 0928-0219, DOI: https://doi.org/10.1515/JIIP.2008.030.

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