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1	New results on the degree of ill-posedness for integration operators with weights Hofmann, Bernd, von Wolfersdorf, Lothar 16 May 2008 (has links) (PDF) We extend our results on the degree of ill-posedness for linear integration opera- tors A with weights mapping in the Hilbert space L^2(0,1), which were published in the journal 'Inverse Problems' in 2005 ([5]). Now we can prove that the degree one also holds for a family of exponential weight functions. In this context, we empha- size that for integration operators with outer weights the use of the operator AA^* is more appropriate for the analysis of eigenvalue problems and the corresponding asymptotics of singular values than the former use of A^*A. Bessel function Compact integral operator Degree of ill-posedness Singular value asymptotics ddc:510 Eigenwertproblem Inverses Problem
2	Ill-Posedness Aspects of Some Nonlinear Inverse Problems and their Linearizations Fleischer, G., Hofmann, B. 30 October 1998 (has links) (PDF) In this paper we deal with aspects of characterizing the ill-posedn ess of nonlinear inverse problems based on the discussion of specific examples. In particular, a parameter identification problem to a second order differential equation and its ill-posed linear components are under consideration. A new approach to the classification ofill-posedness degrees for multiplication operators completes the paper. degree of ill-posedness multiplication op erators nonlinear inverse problems parameter identification MSC 65J20 MSC 47B38 ddc:510
3	Ill-Posedness Aspects of Some Nonlinear Inverse Problems and their Linearizations Fleischer, G., Hofmann, B. 30 October 1998 (has links) In this paper we deal with aspects of characterizing the ill-posedn ess of nonlinear inverse problems based on the discussion of specific examples. In particular, a parameter identification problem to a second order differential equation and its ill-posed linear components are under consideration. A new approach to the classification ofill-posedness degrees for multiplication operators completes the paper. info:eu-repo/classification/ddc/510 ddc:510 degree of ill-posedness multiplication op erators nonlinear inverse problems parameter identification MSC 65J20 MSC 47B38
4	New results on the degree of ill-posedness for integration operators with weights Hofmann, Bernd, von Wolfersdorf, Lothar 16 May 2008 (has links) We extend our results on the degree of ill-posedness for linear integration opera- tors A with weights mapping in the Hilbert space L^2(0,1), which were published in the journal 'Inverse Problems' in 2005 ([5]). Now we can prove that the degree one also holds for a family of exponential weight functions. In this context, we empha- size that for integration operators with outer weights the use of the operator AA^* is more appropriate for the analysis of eigenvalue problems and the corresponding asymptotics of singular values than the former use of A^*A. info:eu-repo/classification/ddc/510 ddc:510 Eigenwertproblem Inverses Problem Bessel function Compact integral operator Degree of ill-posedness Singular value asymptotics

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