
This article is cited in 3 scientific papers (total in 3 papers)
A note on the modulus of continuity for illposed problems in Hilbert space
Bernd Hofmann^{a}, Peter Mathé^{b} ^{a} Department of Mathematics, Chemnitz University of Technology, Chemnitz, Germany
^{b} Weierstraß Institute for Applied Analysis and Stochastics, Berlin, Germany
Abstract:
The authors study linear illposed operator equations in Hilbert space. Such equations become conditionally wellposed by imposing certain smoothness assumptions, often given relative to the operator which governs the equation. Usually this is done in terms of general source conditions. Recently smoothness of an element was given in terms of properties of the distribution function of this element with respect to the selfadjoint associate of the underlying operator. In all cases the original illposed problem becomes wellposed, and properties of the corresponding modulus of continuity are of interest, specifically whether this is a concave function. The authors extend previous concavity results of a function related to the modulus of continuity, and obtained for compact operators in B. Hofmann, P. Mathé, and M. Schieck, Modulus of continuity for conditionally stable illposed problems in Hilbert space, J. Inverse IllPosed Probl. 16 (2008), no. 6, 567–585, to the general case of bounded operators in Hilbert space, and for recently introduced smoothness classes.
Keywords:
illposed, source conditions, individual smoothness, modulus of continuity.
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UDC:
517.983.54 Received: 22.03.2011
Language: English
Citation:
Bernd Hofmann, Peter Mathé, “A note on the modulus of continuity for illposed problems in Hilbert space”, Trudy Inst. Mat. i Mekh. UrO RAN, 18, no. 1, 2012, 34–41
Citation in format AMSBIB
\Bibitem{HofMat12}
\by Bernd~Hofmann, Peter~Math\'e
\paper A note on the modulus of continuity for illposed problems in Hilbert space
\serial Trudy Inst. Mat. i Mekh. UrO RAN
\yr 2012
\vol 18
\issue 1
\pages 3441
\mathnet{http://mi.mathnet.ru/timm777}
\elib{http://elibrary.ru/item.asp?id=17358676}
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Bot R.I., Hofmann B., Mathe P., “Regularizability of IllPosed Problems and the Modulus of Continuity”, Z. Anal. ihre. Anwend., 32:3 (2013), 299–312

Cheng J., Hofmann B., Lu Sh., “the Index Function and Tikhonov Regularization For IllPosed Problems”, J. Comput. Appl. Math., 265 (2014), 110–119

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