5 papers · 1 filter
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…
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…
Norms in sinogram space and stability estimates for the Radon transform
Stefan Kindermann, Simon Hubmer
We consider different norms for the Radon transform of a function and investigate under which conditions they can be estimated from above or below by some standard norms f…
Curious ill-posedness phenomena in the composition of non-compact linear operators in Hilbert spaces
Stefan Kindermann, Bernd Hofmann
We consider the composition of operators with non-closed range in Hilbert spaces and how the nature of ill-posedness is affected by their composition. Specifically, we study the \m…
On the type of ill-posedness of generalized Hilbert matrices and related operators
Stefan Kindermann
We consider infinite-dimensional generalized Hilbert matrices of the form , where are nonnegative weights and are pairwise disjoint…