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Regularizability of ill-posed problems and the modulus of continuity

The regularization of linear ill-posed problems is based on their conditional well-posedness when restricting the problem to certain classes of solutions. Given such class one may consider several related real-valued functions, which measure the wellposedness of the problem on such class. Among those functions the modulus of continuity is best studied. For solution classes which enjoy the additional feature of being star-shaped at zero, the authors develop a series of results with focus on continuity properties of the modulus of continuity. In particular it is highlighted that the problem is conditionally well-posed if and only if the modulus of continuity is right-continuous at zero. Those results are then applied to smoothness classes in Hilbert space. This study concludes with a new perspective on a concavity problem for the modulus of continuity, recently addressed by two of the authors in "Some note on the modulus of continuity for ill-posed problems in Hilbert space", 2011.

Identiferoai:union.ndltd.org:DRESDEN/oai:qucosa.de:bsz:ch1-qucosa-77342
Date17 October 2011
CreatorsBot, Radu Ioan, Hofmann, Bernd, Mathe, Peter
ContributorsTechnische Universität Chemnitz, Fakultät für Mathematik, Technische Universität Chemnitz, Fakultät für Mathematik, Weierstrass-Institut für Angewandte Analysis und Stochastik,, Technische Universität Chemnitz, Fakultät für Mathematik
PublisherUniversitätsbibliothek Chemnitz
Source SetsHochschulschriftenserver (HSSS) der SLUB Dresden
LanguageEnglish
Detected LanguageEnglish
Typedoc-type:preprint
Formatapplication/pdf, text/plain, application/zip
Relationdcterms:isPartOf:Preprintreihe der Fakultät für Mathematik der TU Chemnitz, Preprint 2011-17

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