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New results on the degree of ill-posedness for integration operators with weights

By Bernd Hofmann and Lothar von Wolfersdorf


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

Topics: Bessel function, Compact integral operator, Degree of ill-posedness, Singular value asymptotics, ddc:510, Eigenwertproblem, Inverses Problem
Publisher: Universit├Ątsbibliothek Chemnitz
Year: 2008
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