THE HAUSDORFF MOMENT PROBLEM IN THE LIGHT OF ILL-POSEDNESS OF TYPE I

The Hausdorf moment problem (HMP) over the unit interval in an L 2 -setting is a classical example of ill-posed inverse problem. Since various applications can be rewritten terms HMP, it has gathered significant attention literature. From point view regularization special interest because occurrence non-compact forward operator with non-closed range. Consequently, HMP constitutes one few examples linear type I sense Nashed. In this paper we highlight property and its consequences, for example, existence infinite-dimensional subspace stability. On other hand, show conditional stability estimates Sobolev spaces that indicate severe ill-posedness full recovery function from moments, H ̈older-type excluded. However, associated value at rightmost stable H1 -setting. We moreover discuss truncated where becomes compact. Some numerical case studies illustrate theoretical results complete paper.