The object of this paper is threefold. First, we investigate in a Hilbert space setting the utility
of approximate source conditions in the method of Tikhonov–Phillips regularization for linear …

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 …

We consider compact composite linear operators in Hilbert space, where the composition is
given by some compact operator followed by some non-compact one possessing a non …

Covering ill-posed problems with compact and non-compact operators regarding the degree
of ill-posedness is a never ending story written by many authors in the inverse problems …

Magnetic particle imaging (MPI) is a promising new in vivo medical imaging modality in
which distributions of super-paramagnetic nanoparticles are tracked based on their …

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 …

We present some new ideas and results for finding convergence rates in Tikhonov
regularization for ill‐posed linear inverse problems with compact and non‐compact forward …

Obtaining the temporal shape of an ultrashort laser pulse using the method of dispersion
scan entails solving a nonlinear inverse problem, a challenging prospect on its own, yet still …

We consider infinite-dimensional generalized Hilbert matrices of the form H i, j= didjxi+ xj,
where di are nonnegative weights and xi are pairwise distinct positive numbers. We state …

Linear non-compact operators are difficult to study because they do not exist in the finite
dimensional world. Recently, Math\'{e} and Hofmann studied the singular values of the …