Role of Hilbert scales in regularization theory

Hilbert scales, which are generalizations of Sobolev scales, play crucial roles in the regularization theory. In this paper, it is intended to discuss some important properties of Hilbert scales with illustrations through examples constructed using the concept of Gelfand triples, and using them to describe source conditions and for deriving error estimates in the regularized solutions of ill-posed operator equations. We discuss the above with special emphasis on some of the recent work of the author.