Modulus of continuity for conditionally stable ill-posed problems in Hilbert space

Abstract

One of the fundamental results in the theory of ill-posed inverse problems asserts that these problems can become conditionally well-posed when restricting the domain of the forward operator in an appropriate manner. This leads to the study of certain moduli of continuity for the associated restricted inverse operator. The authors systematically study this modulus of continuity and highlight its intimate connection to error bounds of various regularizing procedures. The contributions of V. K. Ivanov and his concept of quasi-solutions are fundamental for such analysis.