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math.FA2025
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…
math.FA2025
Classification of ill-posedness for bounded linear operators in Banach spaces
Bernd Hofmann, Stefan Kindermann
In this article, concepts of well- and ill-posedness for linear operators in Hilbert and Banach spaces are discussed. While these concepts are well understood in Hilbert spaces, th…
math.FA2025
Operator ordering by ill-posedness in Hilbert and Banach spaces
Stefan Kindermann, Bernd Hofmann
For operators representing ill-posed problems, an ordering by ill-posedness is proposed, where one operator is considered more ill-posed than another one if the former can be expre…