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Journal of Inverse and III-posed Problems

Editor-in-Chief: Kabanikhin, Sergey I.

6 Issues per year

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

B. Hofmann1 / P. Mathé2 / M. Schieck3

1Department of Mathematics, Chemnitz University of Technology, 09107 Chemnitz, Germany. Email:

2Weierstraß Institute for Applied Analysis and Stochastics, Mohrenstraße 39, 10117 Berlin, Germany. Email:

3Department of Mathematics, Chemnitz University of Technology, 09107 Chemnitz, Germany. Email:

Citation Information: Journal of Inverse and Ill-posed Problems. Volume 16, Issue 6, Pages 567–585, ISSN (Online) 1569-3945, ISSN (Print) 0928-0219, DOI: 10.1515/JIIP.2008.030, September 2008

Publication History:
Received:
2008-04-11
Published Online:
2008-09-30

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

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