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Curious ill-posedness phenomena in the composition of non-compact linear operators in Hilbert spaces

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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 \mbox{Hausdorff-,} Ces\`{a}ro-, integration operator, and their adjoints, as
Hofmann, Bernd, Kindermann, Stefan
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