28 citations · 59 across the 10 of their papers we have counts for
5 papers · 1 filter
Duality of uncomplemented null-space and non-closed range and its impact on the regularization of Mazur-type operators
Jens Flemming, Bernd Hofmann
Up to now operators with uncomplemented null-space have been playing only a minor role in regularization theory for ill-posed inverse problems in Banach spaces. We show that ill-po…
A note on the Goldberg-Thorp example in light of the classification of linear ill-posed problems in Banach spaces
Bernd Hofmann, Jens Flemming
This note considers the strictly singular mapping, denoted by , from onto of an example by Goldberg and Thorp from 1963 as a typical hybrid-type operator in th…
New aspects of ill-posedness classification in Banach spaces
Jens Flemming, Bernd Hofmann
Motivated by a seminal paper of professor M. Z. Nashed published in 1987 on classification of ill-posed linear operator equations and distinguishing two types of ill-posedness in B…
Injectivity and weak*-to-weak continuity suffice for convergence rates in -regularization
Jens Flemming, Daniel Gerth
We show that the convergence rate of -regularization for linear ill-posed equations is always if the exact solution is sparse and if the considered operator is injec…
On -regularization in light of Nashed's ill-posedness concept
Jens Flemming, Bernd Hofmann, Ivan Veselic
Based on the powerful tool of variational inequalities, in recent papers convergence rates results on -regularization for ill-posed inverse problems have been formulated in…